Download ScientificNotation. for 8th grade.notebook

ScientificNotation. for 8th grade.notebook
October 09, 2013
Teacher Notes Subject: Math
Topic: Scientific Notation
Title: Scientific Notation
Grade(s): 6, 7and 8
Cross­curricular link(s): Nonspecific
Intended learning outcome(s)
• Students learn how to convert numbers to scientific notation
• Students learn how multiply numbers written in scientific form
• Students learn how to write and multiply numbers less than one in scientific notation
Recommended usage: Introduction or review
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Scientific Notation
Windows(R) operating system and Mac OS X operating system software
Submitted by Candace Beaton
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ScientificNotation. for 8th grade.notebook
October 09, 2013
What is scientific notation?
Use the dictionary link provided and find the definition for scientific
notation. Write the definition below.
The number 154,000,000,000 is written in scientific notation as
exponent
11
1.54 x 10
coefficient
base
The first number (1.54) is called the coefficient. The coefficient must be
greater than or equal to 1 and less than 10.
The second number (10) is called the base. It must always be 10. The base
number 10 is always written in exponent form.
The third number(11) is called the exponent. It is also referred to as the power of ten.
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ScientificNotation. for 8th grade.notebook
172 000 000 000
October 09, 2013
Write this number in scientific notation by
following the steps below.
Step 1: Put the decimal after the first digit.
1.72000000000
Step 2: Find the exponent by counting the number of places from the decimal to the
end of the number.
1.72000000000
1 2 3 4
5 6 7 8 9 10 11
Step 3: Drop the zeros to get the coefficient. Multiply it by the base (which is
always 10) and include the exponent that you found in step 2.
11
1.72 x 10
Write the following numbers in scientific notation using the steps
provided on page 5.
195 000 000 000
675 000 000
Step 1:
Step 1:
Step 2:
Step 2:
Step 3:
Step 3:
56 000 000
Step 1:
Step 2:
Step 3:
72 000
Step 1:
Step 2:
Step 3:
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ScientificNotation. for 8th grade.notebook
October 09, 2013
Complete the following table.
Number
Base
Coefficient
Exponent
123 000 000
98 000
785 000 000 000 000
6.7
10
5
9.46
10
8
Fill in the blanks.
1830000
=
x 10
357000
=
x 10
47100
=
x 10
874000000
=
x 10
7
=
7.89
x 10
9
=
9.235
x 10
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ScientificNotation. for 8th grade.notebook
October 09, 2013
Multiplication in scientific notation
8
4
(2.1 x 10 ) (3.2 x 10 )
Multiply these two numbers together by
following the steps below.
Step 1: Multiply the coefficients together.
2.1 x 3.2 = 6.72
Step 2: Add the exponents together. (Base 10 always remains the same.)
8 + 4 = 12
Step 3: Write the product.
8
4
12
(2.1 x 10 ) (3.2 x 10 ) = 6.72 x 10
Multiply the following using the steps provided on page 9.
3
4
(2 X 10 )(4 X 10 ) =
5
6
(3 X 10 )(2 X 10 ) =
Step 1:
Step 1:
Step 2:
Step 2:
Step 3:
Step 3:
7
4
(5.5 X 10 )(1.1 x 10 ) =
9
5
(2.6 X 10 )(3.1 x 10 ) =
Step 1:
Step 1:
Step 2:
Step 2:
Step 3:
Step 3:
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ScientificNotation. for 8th grade.notebook
October 09, 2013
What happens if the coefficient is more than 10?
3
7
4
Example: (6 x 10 ) (4 x 10 ) = 24 x 10
The product value is not correctly written in scientific notation because the
coefficient is not between 1 and 10. To make it correct, move the decimal point
over to the left until the coefficient is between 1 and 10. For each place you move
the decimal to the left, the exponent will be increased by one power of ten.
4
3
7
8
(6 x 10 ) (4 x 10 ) = 24 x 10 = 2.4 x 10
Multiply the following and put the product in proper scientific
notation.
4
5
8
5
(9.2 x 10 ) (3.1 x 10 ) =
(4.5 x 10 ) (4.2 x 10 ) =
4
9
(7.11 x 10 ) (3 x 10 ) =
2
6
(8.3 x 10 ) (7.2 x 10 ) =
6
ScientificNotation. for 8th grade.notebook
October 09, 2013
How do you do multiplication of scientific notation if the
exponents are negative?
When multiplying numbers in scientific notation that have negative exponents, use
the same steps as before but use the rules of addition of signed numbers.
-3
-3
-6
Example: (2 x 10 ) (3x 10 ) = 6 x 10
Multiply the following numbers:
-4
-6
(3 X 10 )(2X10 ) =
2
-5
(5 X 10 )(1 X 10 ) =
4
-7
(5.5 X 10 )(4.2 x 10 ) =
Division in scientific notation
(2.4 x 106)
(1.2 x 102)
Divide these two numbers by
following the steps below.
Step 1. Divide the two coefficients.
2
1.2 2.4
Step 2: Subtract the exponents. (Base 10 always remains the same.)
6-2=4
Step 3. Write the quotient.
2 x 104
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ScientificNotation. for 8th grade.notebook
October 09, 2013
Use the three steps to solve these problems.
(7.5 x 101)
(2.5 x 104)
(3.9 x 105)
(1.3 x 103)
Step 1.
Step 1.
Step 2.
Step 2.
Step 3.
Step 3.
What happens if the coefficient is less than 1?
(2.5 x 104)
2
=
0.5
x
10
2
(5 x 10 )
The quotient value is not correctly written in scientific notation because the
coefficient is not between 1 and 10. To make it correct, move the decimal point
over to the right until the coefficient is between 1 and 10. For each place you
move the decimal to the right, the exponent will be decreased by one power of ten.
(2.5 x 104)
2
1
=
0.5
x
10
=
5
x
10
2
(5 x 10 )
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ScientificNotation. for 8th grade.notebook
October 09, 2013
Divide the following and put the product in proper scientificnotation.
(1.4 x 105)
(7 x 103)
(2.4 x 107)
(6 x 102)
(1.2 x 10-2)
(1.5 x 102)
Word problems associated with the division
of scientific notation.
1. A pronghorn antelope can travel at a speed of 6 x 101
miles per hour. A snail can travel at a speed of 3 x 10-2
miles per hour. How many times the speed of a nsail is the
speed a pronghorn antelope?
2. The mass of Mercury is 3 x 1023 kg. The mass of
Jupiter is 1.8 x 1027 kg. How many times the mass of
Mercury is the mass of Jupiter?
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ScientificNotation. for 8th grade.notebook
October 09, 2013
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