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PRE-ALGEBRA
Lesson 4-9 Warm-Up
PRE-ALGEBRA
“Scientific Notation”
(4-9)
What is “scientific
notation”?
scientific notation: a way to write very large numbers in short form using powers of 10
in the form a x 10n, where n is an integer and a is between 1 and 10 (1 ≤ a ≤ 10).
Example: 7,500,000,000,000 (“7 trillion, 500 billion”) = 7.5 x 1012
How do you write a
number in scientific
notation?
To write a number in scientific notation, move the decimal so it’s after the first nonzero
(≠ 0) digit, write the rest of the nonzero numbers after the decimal, and multiply this by
10 to the power of the number of jumps it would take to make the original number (right
jumps = positive exponent and left jumps = negative exponent).
__._____ x 10 ___  decimal jumps it would take to make the number
 
first rest of
nonzero the nonzero
digit digits
Standard Notation: the usual way to write a number using commas, etc.
Examples: The world’s largest tree is the General Sherman at, 2,777,000 pounds.Write
this weight in scientific notation.
Move the decimal point to get a number greater than
1 but less than 10.
Drop the zeros after the last nonzero digit
Since you moved the decimal 6 places to the left to
make a smaller number, make the exponent a
positive 6
PRE-ALGEBRA
“Scientific Notation”
(4-9)
Examples: Write 0.000079 in scientific notation.
Move the decimal point to get a number greater than 1 but less
than 10.
Drop the zeros before the first nonzero digit
Since you moved the decimal 5 places to the right to make a
bigger number, make the exponent a negative 5
What is “standard
notation”?
How do you
change scientific
notation to standard
notation?
Standard Notation: the usual way to write a number using commas, etc.
standard notation: the way you normally write numbers using place value
To change scientific notation to standard notation, move the decimal the number of
places the exponent tells you to. Move the decimal to the right for positive exponents
(make a bigger number) and to the left for negative exponents (make number
smaller).
Scientific Notation
Standard Notation
3.6 x 1012 (3.6 trillion)
3,600,000,000,000
4.36 x 10-11
0.0000000000436
PRE-ALGEBRA
Scientific Notation
LESSON 4-9
Additional Examples
About 6,300,000 people visited the Eiffel Tower in
the year 2000. Write this number in scientific notation.
6,300,000
Move the decimal point to get a decimal greater than 1
but less than 10.
6 places
6.3
6.3  106
Drop the zeros after the 3.
You moved the decimal point 6 places. The original
number is greater than 10.Use 6 as the exponent of 10.
PRE-ALGEBRA
Scientific Notation
LESSON 4-9
Additional Examples
Write 0.00037 in scientific notation.
0.00037
Move the decimal point to get a decimal greater than 1
but less than 10.
4 places
3.7
3.7  10–4
Drop the zeros before the 3.
You moved the decimal point 4 places. The original
number is less than 1.Use –4 as the exponent of 10.
PRE-ALGEBRA
Scientific Notation
LESSON 4-9
Additional Examples
Write each number in standard notation.
a. 3.6  104
3.6000
36,000
b. 7.2  10–3
007.2
0.0072
Write zeros while moving the decimal point.
Rewrite in standard notation.
Write zeros while moving the decimal point.
Rewrite in standard notation.
PRE-ALGEBRA
Scientific Notation
LESSON 4-9
Additional Examples
Write each number in scientific notation.
a. 0.107  1012
0.107  1012 = 1.07  10–1  1012
= 1.07  1011
Write 0.107 as
1.07  10–1.
Add the exponents.
b. 515.2  10–4
515.2  10–4 = 5.152  102  10–4
= 5.152  10–2
Write 515.2 as 5.152  102.
Add the exponents.
PRE-ALGEBRA
“Scientific Notation”
(4-9)
How do you
order numbers in
scientific
notation?
To order numbers in scientific notation, order by the exponents only first, If
there is a tie with the exponents, order by the decimal next.
Examples: Order 0.064 x 108 , 312 x 10-4 , and 0.58 x 107 from least to
greatest.
Step 1: Write each number in correct scientific notation.
Step 2: Order the powers of 10 from least to greatest first. Arrange the
decimals with the same power of 10 from least to greatest if necessary.
Step 3: Write the original numbers in order from least to greatest.
PRE-ALGEBRA
Scientific Notation
LESSON 4-9
Additional Examples
Order 0.035  104, 710  10–1, and 0.69  102 from
least to greatest.
Write each number in scientific notation.
0.035  104
3.5  102
710  10–1
0.69  102
7.1  10
6.9  10
Order the powers of 10. Arrange the decimals with the same
power of 10 in order.
6.9  101
7.1  101
3.5  102
Write the original numbers in order.
0.69  102, 710  10–1, 0.035  104
PRE-ALGEBRA
“Scientific Notation”
(4-9)
How do multiply
numbers in
scientific
notation?
To multiply numbers in scientific notation, multiply the decimals and powers
of 10 separately. Then, put the answer in correct scientific notation form.
Examples: The Great Pyramid of Giza in Egypt contains about 2.3 x 106
blocks of stone. On average, each block weighs about 5 x 103 ponds. About
how heavy is the Pyramid?
(2.3 x 106)(5 x 103)
= 2.3 x 5 x 106 x 103
= 11.5 x 106 x 103
= 11.5 x 109
= (1.15 x 101) x 109
= 1.15 x 1010
Multiply the number of blocks by the weight of
each block to find the total weight.
Use the Commutative Property of
Multiplication to rearrange the terms.
Multiply the decimals.
Add the exponents
Write 11.5 x 109 in correct scientific notation
Add the exponents
The Great Pyramid of Giza weighs about 1.15 x 1010 lb.
PRE-ALGEBRA
Scientific Notation
LESSON 4-9
Additional Examples
Multiply 4  10–6 and 7  109. Express the result in
scientific notation.
(4  10–6)(7  109) = 4  7  10–6  109
Use the Commutative
Property of
Multiplication.
= 28  10–6  109
Multiply 4 and 7.
= 28  103
Add the exponents.
= 2.8  101  103
Write 28 as 2.8  101.
= 2.8  104
Add the exponents.
PRE-ALGEBRA
Scientific Notation
LESSON 4-9
Additional Examples
Scientists find a wooly mammoth fossil that is
about 2.0  104 years old. They believe that Earth is
about 2.3  105 times as old as this fossil. How old do
they believe Earth is?
(2.0  104)(2.3  105)
Multiply age of fossil by the
number of times as old as this
fossil Earth is.
= 2.0  2.3  104  105
Use Commutative Property of
Multiplication.
= 4.6  104  105
Multiply 2.0 and 2.3.
= 4.6  109
Add the exponents.
Earth is about 4.6  109 years old.
PRE-ALGEBRA
Scientific Notation
LESSON 4-9
Lesson Quiz
Write each number in scientific notation.
1. 5,400,000
2. 0.0000867
5.4  106
8.67  10–5
Write each number in standard notation.
3. 3.45  106
3,450,000
4. 1.99  10–5
0.0000199
5. Order 7.2  105, 7.2  106, 7.02  106, and 7.1  10–6 from least
to greatest.
7.1  10–6, 7.2  105, 7.02  106, 7.2  106
6. Multiply 14  106 and 4  10–4. Express the result in scientific
notation.
5.6  103
PRE-ALGEBRA