Download Document

Slide 1 / 139
Slide 2 / 139
Scientific Notation
8th Grade
2015-01-15
www.njctl.org
Slide 3 / 139
Slide 4 / 139
Table of Contents
Links to PARCC sample questions
Click on the topic to go to that section
· The purpose of scientific notation
· How to write numbers in scientific notation
· How to convert between scientific notation and standard form
Non-Calculator 5
Calculator 13
· Magnitude
· Comparing numbers in scientific notation
· Multiply and Divide with scientific notation
· Addition and Subtraction with scientific notation
· Glossary
Slide 5 / 139
Vocabulary words are identified with a
dotted underline.
Slide 6 / 139
The charts have 4 parts.
1
Sometimes when you subtract the fractions,
you find that you can't because the first
numerator is smaller than the second! When
this happens, you need to regroup from the
whole number.
(Click on the dotted
underline.)
A whole number
that can divide into
another number
with no remainder.
15
How many fifths are in 1 whole?
The underline is linked to the glossary at the end of the
Notebook. It can also be printed for a word wall.
2
Its meaning
How many thirds are in 1 whole?
How many ninths are in 1 whole?
Factor
Vocab Word
3
Examples/
Counterexamples
(As it is used
in the
lesson.)
5 R.1
3 16
5
3 is a factor of 15
3
A whole number
that multiplies with
another number to
make a third number.
3 x 5 = 15
3 is not a
factor of 16
Back to
3 and 5 are
factors of 15
4
Instruction
Link to return to the
instructional page.
Slide 7 / 139
Slide 8 / 139
Can you match these BIG objects
to their weights?
Purpose of Scientific Notation
The Great Pyramid at Giza
The Earth
300,000,000,000 kg
Scientists are often confronted with numbers that look like this:
2,000,000,000,000,000,
300,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 kg
000 kg
Blue Whale - largest animal on earth
600,000,000 kg
Can you guess what weighs this much?
60,000,000,000,000,
000,000,000,000 kg
Return to
Table of
Contents
Slide 9 / 139
The Sun
Total Human Population
180,000 kg
Slide 10 / 139
Can you match these BIG objects
to their weights?
Can you match these small
objects to their weights?
grain of sand
600,000,000 kg
60,000,000,000,000,
000,000,000,000 kg
Click object
to reveal
answer
0.00015 kg
Blue Whale - largest animal on earth
180,000 kg
molecule
0.000000000000000000000000030 kg
steam
2,000,000,000,000,000,
000,000,000,000,000 kg 300,000,000,000 kg
Slide 11 / 139
0.00000000035 kg
Slide 12 / 139
Click to reveal answers.
grain of sand
Scientific Notation
The examples were written in "standard form", the form we
normally use. But the standard form is difficult to work with
when a number is HUGE or tiny, if it has a lot of zeros.
0.00000000035 kg
molecule
Scientists have come up with a more convenient method to
write very LARGE and very small numbers.
0.000000000000000000000000030 kg
steam
0.00015 kg
Writing numbers in scientific notation doesn't
change the value of the number.
Slide 13 / 139
Slide 14 / 139
Powers of Ten
Scientific Notation
101 = 10
102 = 10 x 10 = 100
Scientific Notation uses Powers of 10 to write big or small
numbers more conveniently.
103 = 10 x 10 x 10 = 1,000
104 = 10 x 10 x 10 x 10 = 10,000
Using scientific notation requires us to use the rules of
exponents we learned earlier. While we developed those
rules for all bases, scientific notation only uses base 10.
105 = 10 x 10 x 10 x 10 x 10 = 100,000
click here to see a video on powers of ten
which puts our universe into perspective!
click here to move from the Milky Way
through space towards Earth to a oak tree,
and then within a cell !
Slide 15 / 139
Slide 16 / 139
Exponent Rules
Powers of Integers
Remember that when multiplying numbers with exponents, if
the bases are the same, you write the base and add the
exponents.
Powers are a quick way to write repeated multiplication,
just as multiplication was a quick way to write repeated
addition.
25 x 26 = 2(5+6) = 211
These are all equivalent:
33 x 37 = 3
103
(10)(10)(10)
1000
(3+7)
= 310
108 x 10-3 = 10(8+-3) = 105
In this case, the base is 10 and the exponent is 3.
47 x 4-7 = 4(7+-7) = 40 = 1
Slide 17 / 139
1
102 x 104 =
Slide 18 / 139
2
1014 x 10-6 =
A
106
A
106
B
108
B
108
C
10
10
C
1010
D
1012
D
1012
Slide 19 / 139
3
Slide 20 / 139
4
10-4 x 10-6 =
104 x 10 6 =
A
10-6
A
106
B
10
B
108
C
10-10
C
1010
D
10-12
D
1012
-8
Slide 21 / 139
Slide 22 / 139
Writing Large
Numbers in
Scientific Notation
Writing Numbers
in Scientific
Notation
Return to
Table of
Contents
Slide 23 / 139
Scientific Notation
Here are some different ways of writing 6,500.
6,500 = 6.5 thousand
6.5 thousand = 6.5 x 1,000
6.5 x 1,000 = 6.5 x 103
which means that 6,500 = 6.5 x 103
6,500 is standard form of the number and 6.5 x 103 is scientific
notation
These are two ways of writing the same number.
Slide 24 / 139
Scientific Notation
6.5 x 103 isn't a lot more convenient than 6,500.
But let's do the same thing with 7,400,000,000
which is equal to 7.4 billion
which is 7.4 x 1,000,000,000
which is 7.4 x 109
Besides being shorter than 7,400,000,000 it is a lot easier to keep track
of the zeros in scientific notation.
And we'll see that the math gets a lot easier as well.
Slide 25 / 139
Slide 26 / 139
Scientific Notation
Scientific notation expresses numbers as the product of:
a coefficientand 10 raised tosome power.
3.78x 106
The coefficient is always greater than or equal to one, and less than 10.
In this case, the number 3,780,000 is expressed in scientific notation.
Express 870,000 in scientific notation
1. Write the number without the comma.
870000
2. Place the decimal so that the first number
will be less than 10 but greater than or equal
to 1.
870000
x 10
.
3. Count how many places you had to move
the decimal point. This becomes the exponent
of 10.
870000
x 10
.
4. Drop the zeros to the right of the right-most
non-zero digit.
8.7 x 105
Slide 27 / 139
Express 53,600 in scientific notation
2
1
Express 284,000,000 in scientific notation
1. Write the number without the comma.
1. Write the number without the comma.
2. Place the decimal so that the first number
will be less than 10 but greater than or equal
to 1.
2. Place the decimal so that the first number
will be less than 10 but greater than or equal
to 1.
3. Count how many places you had to move
the decimal point. This becomes the exponent
of 10.
3. Count how many places you had to move
the decimal point. This becomes the exponent
of 10.
4. Drop the zeros to the right of the right-most
non-zero digit.
4. Drop the zeros to the right of the right-most
non-zero digit.
Which is the correct coefficient of 147,000 when it is
written in scientific notation?
4 3
Slide 28 / 139
Slide 29 / 139
5
5
Slide 30 / 139
6
Which is the correct coefficient of 23,400,000
when it is written in scientific notation?
A 147
A .234
B 14.7
B 2.34
C 1.47
C 234.
D .147
D 23.4
Slide 31 / 139
7
How many places do you need to move the
decimal point to change 190,000 to 1.9?
Slide 32 / 139
8
A 3
How many places do you need to move the
decimal point to change 765,200,000,000 to 7.652?
A 11
B 4
B 10
C 5
C 9
D 6
D 8
Slide 33 / 139
9
Which of the following is 345,000,000 in scientific
notation?
A 3.45 x 10
8
B 3.45 x 10
6
Slide 34 / 139
10
Which of these numbers, written in scientific
notation, is not a number greater than one ?
A .34 x 10 8
B 7.2 x 10 3
C 8.9 x 10 4
C 345 x 10 6
D 2.2 x 10 -1
D .345 x 10 9
E
11.4 x 1012
F .41 x 10 3
Slide 35 / 139
Slide 36 / 139
The mass of the solar system
300,000,000,000,000,
000,000,000,000,000,
000,000,000,000,000,
000,000,000 kg
(How do you even say
that number?)
More Practice
Slide 37 / 139
Express 9,040,000,000 in scientific notation
Slide 38 / 139
Express 13,030,000 in scientific notation
1. Write the number without the comma.
1. Write the number without the comma.
2. Place the decimal so that the first number
will be less than 10 but greater than or equal
to 1.
2. Place the decimal so that the first number
will be less than 10 but greater than or equal
to 1.
3. Count how many places you had to move
the decimal point. This becomes the exponent
of 10.
3. Count how many places you had to move
the decimal point. This becomes the exponent
of 10.
4. Drop the zeros to the right of the right-most
non-zero digit.
4. Drop the zeros to the right of the right-most
non-zero digit.
Slide 39 / 139
Express 1,000,000,000 in scientific notation
1. Write the number without the comma.
2. Place the decimal so that the first number
will be less than 10 but greater than or equal
to 1.
3. Count how many places you had to move
the decimal point. This becomes the exponent
of 10.
Slide 40 / 139
11
Which of the following is 12,300,000 in scientific
notation?
A .123 x 10 8
B 1.23 x 10 5
C 123 x 10 5
D 1.23 x 10 7
4. Drop the zeros to the right of the right-most
non-zero digit.
Slide 41 / 139
Slide 42 / 139
Express 0.0043 in scientific notation
1. Write the number without the decimal point.
Writing Small Numbers
in
Scientific Notation
2. Place the decimal so that the first number is 1 or
more, but less than 10.
3. Count how many places you had to move the
decimal point. The negative of this number
becomes the exponent of 10.
4. Drop the zeros to the left of the left-most nonzero digit.
0043
?
0043
. x 10
?
0043
. x 10
1
2 3
4.3 x 10-3
Slide 43 / 139
Slide 44 / 139
Express 0.0073 in scientific notation
Express 0.00000832 in scientific notation
1. Write the number without the decimal point.
1. Write the number without the decimal point.
2. Place the decimal so that the first number is 1 or
more, but less than 10.
2. Place the decimal so that the first number is 1 or
more, but less than 10.
3. Count how many places you had to move the
decimal point. The negative of this numbers
becomes the exponent of 10.
3. Count how many places you had to move the
decimal point. The negative of this numbers
becomes the exponent of 10.
4. Drop the zeros to the left of the left-most nonzero digit.
4. Drop the zeros to the left of the left-most nonzero digit.
Slide 45 / 139
Slide 46 / 139
Scientific Notation: The Difference
Between Positive & Negative Exponents
12
A 832
As you get further and further down a number line in the positive
direction, your numbers are getting bigger. Therefore, really big
numbers will have a positive exponent when written in scientific
notation.
B 83.2
C .832
D 8.32
0 20 40 60 80 100 120 140 160 180 200
As you get further and further down a number line in the negative
direction, your numbers are getting smaller. Therefore, really small
numbers will have a negative exponent when written in scientific
notation.
-200 -180 -160 -140 -120 -100 -80 -60 -40 -20
Which is the correct decimal placement to convert
0.000832 to scientific notation?
0
Slide 47 / 139
13
Which is the correct decimal placement to convert
0.000000376 to scientific notation?
Slide 48 / 139
14
How many times do you need to move the decimal
point to change 0.00658 to 6.58?
A 3.76
A 2
B 0.376
B 3
C 376.
C 4
D 37.6
D 5
Slide 49 / 139
15
How many times do you need to move the decimal
point to change 0.000003242 to 3.242?
16
Write 0.00278 in scientific notation.
A 27.8 x 10 -4
A 5
B 2.78 x 10 3
B 6
C 2.78 x 10 -3
C 7
D 278 x 10 -3
D 8
Slide 51 / 139
17
Slide 50 / 139
Slide 52 / 139
Which of these numbers, written in scientific
notation, is a number greater than one?
A .34 x 10 -8
More Practice
B 7.2 x 10 -3
C 8.9 x 10 4
D 2.2 x 10 -1
E
11.4 x 10-12
F .41 x 10 -3
Slide 53 / 139
Express 0.001003 in scientific notation
Slide 54 / 139
Express 0.000902 in scientific notation
1. Write the number without the decimal point.
1. Write the number without the decimal point.
2. Place the decimal so that the first number is 1 or
more, but less than 10.
2. Place the decimal so that the first number is 1 or
more, but less than 10.
3. Count how many places you had to move the
decimal point. The negative of this numbers
becomes the exponent of 10.
3. Count how many places you had to move the
decimal point. The negative of this numbers
becomes the exponent of 10.
4. Drop the zeros to the left of the left-most nonzero digit.
4. Drop the zeros to the left of the left-most nonzero digit.
Slide 55 / 139
Slide 56 / 139
Express 0.0000012 in scientific notation
18
Write 0.000847 in scientific notation.
1. Write the number without the decimal point.
A 8.47 x 10 4
2. Place the decimal so that the first number is 1 or
more, but less than 10.
B 847 x 10 -4
C 8.47 x 10 -4
D 84.7 x 10 -5
3. Count how many places you had to move the
decimal point. The negative of this numbers
becomes the exponent of 10.
4. Drop the zeros to the left of the left-most nonzero digit.
Slide 57 / 139
Slide 58 / 139
Express 3.5 x 10 4 in standard form
Converting
to
Standard Form
Return to
Table of
Contents
1. Write the coefficient.
3.5
2. Add a number of zeros equal to the
exponent: to the right for positive
exponents and to the left for negative.
3.50000
3. Move the decimal the number of places
indicated by the exponent: to the right for
positive exponents and to the left for
negative.
35000.0
4. Drop unnecessary zeros and add
comma, as necessary.
35,000
Slide 59 / 139
Express 1.02 x 10 in standard form
6
Slide 60 / 139
Express 3.42 x 10 in standard form
-3
1. Write the coefficient.
1. Write the coefficient.
2. Add a number of zeros equal to the
exponent: to the right for positive
exponents and to the left for negative.
2. Add a number of zeros equal to the
exponent: to the right for positive
exponents and to the left for negative.
3. Move the decimal the number of places
indicated by the exponent: to the right for
positive exponents and to the left for
negative.
3. Move the decimal the number of places
indicated by the exponent: to the right for
positive exponents and to the left for
negative.
4. Drop unnecessary zeros and add
comma, as necessary.
4. Drop unnecessary zeros and add
comma, as necessary.
Slide 61 / 139
Express 2.95 x 10 in standard form
-4
Slide 62 / 139
19
1. Write the coefficient.
2. Add a number of zeros equal to the
exponent: to the right for positive
exponents and to the left for negative.
How many times do you need to move the decimal
and which direction to change 7.41 x 10 -6 into
standard form?
A 6 to the right
B 6 to the left
3. Move the decimal the number of places
indicated by the exponent: to the right for
positive exponents and to the left for
negative.
C 7 to the right
D 7 to the left
4. Drop unnecessary zeros and add
comma, as necessary.
Slide 63 / 139
20
How many times do you need to move the decimal
and which direction to change 4.5 x 10 10 into
standard form?
Slide 64 / 139
21
Write 6.46 x 10 4 in standard form.
A 646,000
B 0.00000646
A 10 to the right
C 64,600
B 10 to the left
D 0.0000646
C 11 to the right
D 11 to the left
Slide 65 / 139
22
Write 3.4 x 10 3 in standard form.
Slide 66 / 139
23
Write 6.46 x 10 -5 in standard form.
A 3,400
A 646,000
B 340
B 0.00000646
C 34,000
C 0.00646
D 0.0034
D 0.0000646
Slide 67 / 139
24
Write 1.25 x 10 -4 in standard form.
25
Write 4.56 x 10 -2 in standard form.
A 125
A 456
B 0.000125
B 4560
C 0.00000125
C 0.00456
D 4.125
D 0.0456
Slide 69 / 139
26
Slide 68 / 139
Write 1.01 x 10 9 in standard form.
A 101,000,000,000
B 1,010,000,000
Slide 70 / 139
Using a Calculator for Scientific Notation
When entering numbers into a calculator that are in scientific notation,
you can use the EE button. It means "x 10 to the power of".
C 0.00000000101
D 0.000000101
This button eliminates
the "x 10" of a number
in scientific notation.
So 9 x 108 is entered
into the calculator
using 9 EE 8 and
shows up at the top as
9E8.
Slide 71 / 139
Using a Calculator for Scientific Notation
Slide 72 / 139
Using a Calculator for Scientific Notation
Enter the following numbers into the calculator using the "EE"
button to determine its value in standard form.
a) 4 x 102
b) 5.7 x 10-3
c) 9.87 x 104
d) 1.43 x 10-1
When reading a calculator that
has a number in scientific
notation, remember that the "E"
stands for "x 10 to the power of".
Which number written in standard
form represents the number in
the calculator below?
3.2E9
Slide 73 / 139
Using a Calculator for Scientific Notation
When reading a calculator that
has a number in scientific
notation, remember that the "E"
stands for "x 10 to the power of".
4.21E-11
Slide 74 / 139
27 Which number written in standard form represents
the number in the calculator below?
A 0.000000000482
B 0.0000000000482
C 4,820,000,000,000
Which number written in standard
form represents the number in the
calculator below?
D 48,200,000,000
Slide 75 / 139
28 Which number written in standard form represents
the number in the calculator below?
A 0.000000653
B 0.00000653
Slide 76 / 139
29 Which number written in standard form represents
the number in the calculator below?
A 0.000000000974
6.53E-6
B 0.0000000000974
C 6,530,000
C 9,740,000,000,000
D 653,000,000
D 97,400,000,000
Slide 77 / 139
30 Which number written in standard form represents
the number in the calculator below?
A 0.00000407
B 0.000000407
4.82E10
Slide 78 / 139
31 Liz saw this number on her calculator screen. Which
numbers represent the number Liz saw?
A 0.0000006
4.07E6
9.74E-10
B 0.00000006
C 4,070,000
C -6,000,000
D 407,000,000
D -60,000,000
From PARCC sample test
Slide 79 / 139
Slide 80 / 139
Magnitude
Scientific notation always uses decimal notation that is bigger
than 1 but smaller than 10. Why?
Magnitude
This is due to magnitude. Magnitude is how we can observe
very large or very small numbers and easily compare them.
The magnitude of a number is the exponent when the number
is written in scientific notation. Below are a few examples.
8304 = 8.304 x 103 - the order of magnitude is 3
Return to
Table of
Contents
20,000 = 2 x 104 – the order of magnitude is 4
0.000034 = 3.4 x 10-5 – the order of magnitude is -5
Slide 81 / 139
Slide 82 / 139
Write each of the following in Scientific Notation first and
then indicate the order of magnitude.
Scientific Notation
Order of Magnitude
6214
Application
Let J represent the world population in 1950.
J = 2,556,000,053.
Find the smallest power of 10 that will exceed J.
472.17
The number above (J) has 10 digits and is smaller than a
whole number with 11 digits.
813000000
.000253
(10,000,000,000 or 1010 therefore J<1010)
.00647
The answer is 10.
.00000049
Slide 83 / 139
Application
Let K represent the national debt in 1950.
Slide 84 / 139
32 If m = 149,162,536,496,481,100 find the smallest
power of 10 that will exceed m.
K = 257,357,352,351.
Find the smallest power of 10 that will exceed K.
(
(Derived from
Slide 85 / 139
Slide 86 / 139
33 What is the smallest power of 10 that will exceed
5,321?
(Derived from
find the smallest power of 10 that will
(
(
(Derived from
34 If m = 628
exceed m?
Slide 87 / 139
Slide 88 / 139
35 What would the negative exponent be used to
express the number
?
36 The chance of a shark bite is
and the chance
of dying from a snake bite is
which are more
likely to be bit by?
A both a the same
B the snake
C the shark
D neither
(
(Derived from
Slide 89 / 139
(
(Derived from
Slide 90 / 139
Click for web site
Comparing Numbers
Written in
Scientific Notation
Return to
Table of
Contents
Slide 91 / 139
Comparing numbers in scientific notation
When the exponents are different, just compare the
exponents.
Answer
Comparing numbers in scientific notation
Slide 92 / 139
First, compare the exponents.
Whichever number has the larger exponent is the larger number.
=
<
If the exponents are different, the coefficients don't matter; they
have a smaller effect.
>
9.99 x 10 3
2.17 x 10 4
1.02 x 10 2
8.54 x 10 -3
6.83 x 10 -9
3.93 x 10 -2
just drag the sign
that is correct
Slide 93 / 139
Slide 94 / 139
Comparing numbers in scientific notation
Comparing numbers in scientific notation
If the exponents are the same, compare the coefficients.
When the exponents are the same, just compare the
The larger the coefficient, the larger the number
(if the exponents are the same).
>
5.67 x 103
4.67 x 103
4.32 x 106
4.67 x 106
2.32 x 1010
3.23 x 1010
Slide 95 / 139
37 Which is ordered from least to greatest?
=
<
coefficients.
Slide 96 / 139
38 Which is ordered from least to greatest?
A I, II, III, IV
I. 1.0 x 10 5
A I, II, III, IV
I. 1.0 x 102
B IV, III, I, II
II. 7.5 x 10 6
B IV, III, I, II
II. 7.5 x 10 6
C I, IV, II, III
III. 8.3 x 10 4
C I, IV, II, III
III. 8.3 x 10 9
D III, I, II, IV
IV. 5.4 x 107
D I, II, IV, III
IV. 5.4 x 107
Slide 97 / 139
39 Which is ordered from least to greatest?
Slide 98 / 139
40 Which is ordered from least to greatest?
A I, II, III, IV
I. 1 x 102
A II, III, I, IV
I. 1 x 10-2
B IV, III, I, II
II. 7.5 x 103
B IV, III, I, II
II. 7.5 x 10-24
C III, IV, II, I
III. 8.3 x 10-2
C III, IV, II, I
III. 8.3 x 10-15
D III, IV, I, II
IV. 5.4 x 10-3
D III, IV, I, II
Slide 99 / 139
41 Which is ordered from least to greatest?
IV. 5.4 x 102
Slide 100 / 139
42 Which is ordered from least to greatest?
A I, II, III, IV
I. 1.0 x 102
A I, II, III, IV
I. 1.0 x 106
B IV, III, I, II
II. 7.5 x 102
B IV, III, I, II
II. 7.5 x 106
C I, IV, II, III
III. 8.3 x 102
C I, IV, II, III
III. 8.3 x 106
D III, IV, I, II
IV. 5.4 x 102
D III, IV, I, II
Slide 101 / 139
43 Which is ordered from least to greatest?
IV. 5.4 x 107
Slide 102 / 139
44 Which is ordered from least to greatest?
A I, II, III, IV
I. 1.0 x 103
A I, II, III, IV
I. 2.5 x 10-3
B IV, III, I, II
II. 5.0 x 103
B IV, III, I, II
II. 5.0 x 10-3
C I, IV, II, III
III. 8.3 x 106
C I, IV, II, III
III. 9.2 x 10-6
D III, IV, I, II
IV. 9.5 x 106
D III, IV, I, II
IV. 4.2 x 10-6
Slide 103 / 139
Slide 104 / 139
Multiplying Numbers in Scientific Notation
Multiplying Numbers in
Scientific Notation
Evaluate: (6.0 x 104 )(2.5 x 102 )
Multiplying with scientific notation requires at least three
(and sometimes four) steps.
1. Multiply the coefficients
2. Multiply the powers of ten
applying the rule of exponents
3. Combine those results
4. Put in proper form
1. Multiply the coefficients
6.0 x 2.5 = 15
2. Multiply the powers of ten
applying the rule of exponents
104 x 102 = 106
3. Combine those results
15 x 106
4. Put in proper form
1.5 x 107
Return to
Table of
Contents
Slide 105 / 139
Multiplying Numbers in Scientific Notation
Evaluate: (4.80 x 106 )(9.0 x 10-8 )
1. Multiply the coefficients
2. Multiply the powers of ten
applying the rule of exponents
3. Combine those results
Slide 106 / 139
45 Evaluate (2.0 x 10 -4)(4.0 x 107). Express
the result in scientific notation.
A
8.0 x 10 11
B
8.0 x 103
C
5.0 x 103
D
5.0 x 10 11
E
7.68 x 10-28
F
7.68 x 10-28
4. Put in proper form
Slide 107 / 139
46 Evaluate (5.0 x 10 6 )(7.0 x 10 7 )
Slide 108 / 139
47 Evaluate (6.0 x 10 2 )(2.0 x 10 3 )
A
3.5 x 10 13
A 1.2 x 10 6
B
3.5 x 10
B 1.2 x 10 1
C
3.5 x 10 1
C 1.2 x 10 5
D
3.5 x 10 -1
D 3.0 x 10 -1
E
7.1 x 10 13
E 3.0 x 10 5
F
7.1 x 10 1
F 3.0 x 10 1
14
Slide 109 / 139
48 Evaluate (1.2 x 10 -6 )(2.5 x 10 3 ). Express the
result in scientific notation.
Slide 110 / 139
49 Evaluate (1.1 x 104)(3.4 x 106). Express the result in
scientific notation.
A 3 x 10 3
B 3 x 10 -3
A
3.74 x 1024
B
3.74 x 1010
C 30 x 10 -3
C
4.5 x 1024
D 0.3 x 10 -18
D
4.5 x 1010
E 30 x 10
E
37.4 x 1024
18
Slide 111 / 139
50 Evaluate (3.3 x 10 4 )(9.6 x 10 3 ). Express the result in
scientific notation.
A 31.68 x 10 7
B 3.168 x 10
C 3.2 x 10
Slide 112 / 139
51 Evaluate (2.2 x 10 -5 )(4.6 x 10 -4 ). Express the result in
scientific notation.
A 10.12 x 10 -20
8
B 10.12 x 10 -9
C 1.012 x 10 -10
7
D 32 x 10 8
D 1.012 x 10 -9
30 x 10 7
E 1.012 x 10 -8
E
Slide 113 / 139
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules
as multiplying.
1. Divide the coefficients
2. Divide the powers of ten
applying the rule of exponents
3. Combine those results
4. Put in proper form
Slide 114 / 139
Division with Scientific Notation
Evaluate: 5.4 x 106
9.0 x 102
1. Divide the coefficients
5.4 ÷ 9.0 = 0.6
2. Divide the powers of ten
applying the rule of exponents
106 ÷ 102 = 104
3. Combine those results
0.6 x 104
4. Put in proper form
6.0 x 103
Slide 115 / 139
Division with Scientific Notation
Evaluate:
4.4 x 106
Slide 116 / 139
52 Evaluate
4.16 x 10
5.2 x 10
Express the result in scientific notation.
-9
-5
1.1 x 10
-3
A 0.8 x 10 -4
1. Divide the coefficients
2. Divide the powers of ten
applying the rule of exponents
B 0.8 x 10 -14
C 0.8 x 10 -5
3. Combine those results
D 8 x 10 -4
4. Put in proper form
E
8 x 10 -5
Slide 117 / 139
53 Evaluate
7.6 x 10
4 x 10
Express the result in scientific notation.
-2
-4
Slide 118 / 139
54 Evaluate
8.2 x 10
2 x 10
Express the result in scientific notation.
A 1.9 x 10 -2
A
4.1 x 10 -10
B 1.9 x 10 -6
B
4.1 x 10 4
C 1.9 x 10 2
C
4.1 x 10 -4
D 1.9 x 10
-8
D
4.1 x 10 21
1.9 x 10 8
E
4.1 x 10 10
E
Slide 119 / 139
55 Evaluate
3.2 x 10
6.4 x 10
Express the result in scientific notation.
-2
-4
3
7
Slide 120 / 139
56 The point on a pin has a diameter of approximately
1 x 10 meters. If an atom has a diameter of
2 x 10 meters, about how many atoms could fit
across the diameter of the point of a pin?
-4
-10
A .5 x 10 -6
B .5 x 10 -2
A
50,000
C .5 x 10 2
B
500,000
D 5 x 10 1
C
2,000,000
E
D
5,000,000
5 x 10
3
Question from ADP Algebra I
End-of-Course Practice Test
Slide 121 / 139
Slide 122 / 139
57 The body of a 154 pound person contains
approximately 2 X 10-1 milligrams of gold and 6 X 101
milligrams of aluminum. Based on this information,
the number of milligrams of aluminum in the body is
how many times the number of milligrams of gold in
the body?
Addition and Subtraction
with Scientific Notation
Numbers in scientific notation can only be added or subtracted if
they have the same exponents.
If needed, an intermediary step is to rewrite one of the numbers so
it has the same exponent as the other.
Return to
Table of
Contents
From PARCC sample test
Slide 123 / 139
Slide 124 / 139
Addition and Subtraction
This problem is slightly more difficult because you need to add
one extra step at the end.
This is the simplest example of addition
4.0 x 10 + 5.3 x 10 =
3
Addition and Subtraction
3
8.0 x 10 + 5.3 x 10 =
3
Since the exponents are the same (3), just add the coefficients.
4.0 x 10 + 5.3 x 10 = 9.3 x 10
3
3
3
Since the exponents are the same (3), just add the
coefficients.
This just says
8.0 x 10 + 5.3 x 10 = 13.3 x 10
3
4.0 thousand
+ 5.3 thousand
9.3 thousand.
8.0 x 104 + 5.3 x 103 =
This requires an extra step at the beginning because the
exponents are different. We have to either convert the first
number to 80 x 103 or the second one to 0.53 x 104 .
The latter approach saves us a step at the end.
8.0 x 104 + 0.53 x 104 = 8.53 x 104
Once both numbers had the same exponents, we just add the
coefficient. Note that when we made the exponent 1 bigger,
that's makes the number 10x bigger; we had to make the
coefficient 1/10 as large to keep the number the same.
3
3
But that is not proper form, since 13.3 > 10;
it should be written as 1.33 x 10
4
Slide 125 / 139
Addition and Subtraction
3
Slide 126 / 139
58 The sum of 5.6 x 10 3 and 2.4 x 10 3 is
A
8.0 x 10 3
B
8.0 x 10 6
C
8.0 x 10 -3
D
8.53 x 10 3
Slide 127 / 139
Slide 128 / 139
59 8.0 x 103 minus 2.0 x 103 is
60 7.0 x 103 plus 2.0 x 102 is
A
6.0 x 10-3
A
9.0 x 103
B
0
6.0 x 10
B
9.0 x 105
C
6.0 x 103
C
7.2 x 103
D
7.8 x 103
D
7.2 x 102
Slide 129 / 139
Slide 130 / 139
61 3.5 x 105 plus 7.8 x 105 is
A
11.3 x 105
B
1.13 x 104
C
1.13 x 106
D
11.3 x 1010
Glossary
Return to
Table of
Contents
Slide 131 / 139
Slide 132 / 139
Base
Coefficient
The number that is going to be
raised to a power. It is multiplied the
number of times shown in the power.
188
335
7
3
215
29
112
4
A number used
to multiply a
variable.
In scientific notation,
ten to the power of 3
103 =
the base will always
= 10
10 x 10 x 10 =
1,000
Back to
Instruction
3y 19z
6.5 x 103
A factor of a term.
scientific notation:
.000000459
a coefficient
and 10 raised to
some power
3.78 x 106
4.59 x 10-7
Back to
Instruction
Slide 133 / 139
Slide 134 / 139
Power
Blue Whale
A convenient system scientists developed
to rewrite big or small numbers using
powers of 10 that does not change the value.
A number that shows you A quick way to write
how many times to use the
repeated
number in a multiplication.
multiplication.
a.k.a.
scientific notation:
Exponent
big numbers
a coefficient
180,000 kg =
and 10 raised to
or
ten to the power of 3
Index
103 =
some power
1.8 x 105
3.78 x 106
10 x 10 x 10 =
1,000
Scientific Notation
Back to
small numbers
a coefficient
and 10 raised to
some power.
0.00015 kg =
3.78 x 106
1.5 x 10-4
Instruction
Slide 135 / 139
Back to
Instruction
Slide 136 / 139
Standard Form
A number whose
scientific form has
been expanded.
4,500,000
0.00000032
0.006789
120,000
The most
familiar form of
a number.
Standard Form:
6,500
vs.
Scientific Form:
6.5 x 103
*Note* this is
not the
"correct" form
but the most
recognizable
form.
Back to
Back to
Instruction
Instruction
Slide 137 / 139
Slide 138 / 139
Back to
Back to
Instruction
Instruction
Slide 139 / 139
Back to
Instruction