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8.5 Scientific Notation
Algebra 1 Concepts and Skills McDougal Littell Linda Stamper
The exponent tells about the size of the number.
A positive exponent indicates a number greater than or equal to 1.
A negative exponent indicates a number between zero and 1.
Scientific notation is a shorthand way of writing numbers that are very large or very small. Scientific notation has 3 parts.
a number greater than or equal to 1, but less than 10
Xmultiplication symbol – do not use multiplication dot
a power of 10
101.2512.5.125
Rules to Write in Standard NotationIf the exponent is positive, move the decimal point as
many places to the right as indicated by the exponent.
1.120000
1.12 x 106
. 1,120,000positive exponent large number
If the exponent is negative, move the decimal point as many places to the left as indicated by the exponent.
4.3 x 10-4 0004.3
.00043
negative exponent small number
.
Example 1 Write in standard notation (decimal form).1. Write problem.
3.0259 x 108
2. Write standard form.
000,590,302
PracticeA. 6.7 x 105
B. 1.38 x 10-4
C. 6.12 x 10-5
D. 5.4 x 104
= 670,000 = .000138 = .0000612 = 54,000
Rules to Write in Scientific NotationMove the decimal point to create a number greater than or
equal to 1 and less than 10. Count the decimal positions to identify the exponent. If the original number is greater than or equal to 1, the exponent is positive. If the original number is between zero and 1, the exponent is negative.
3.25 x 1063,250,000•use a positive
exponent original number is > 1
0.000817 8.17 x 10-
4
use a negative exponent original
number is between 0 and 1
•
•
Example 2 Write in scientific notation.
1. Write problem.
42,000,000
2. Write scientific notation.
710 x 2.4
PracticeA. 0.000052B. 3,107,000C. 970,000,00
0D. 0.0063
= 5.2 x 10-5 = 3.107 x 106 = 9.7 x 108
= 6.3 x 10-3
What do you already know about the sign
of the exponent?
Operations with Scientific Notation 36 10 x 410 x 3
Group the whole/decimal numbers together.
4 x 3
Group the powers of 10 together.
36 10 x10
Simplify within each group.
12
Write the whole/decimal number in scientific notation.
10 x 2.1 1
Combine the powers of ten.
9110 x 2.1
What property says you
can do this?
3610 x
910 x 12 10 x 9
1010 x 2.1
What do you know about the size of
this number?
Example 3 Perform the indicated operation. Write the result in scientific notation.
53 10 x 210 x 3
2. Group the whole/decimal numbers together.
2 x 3
Group the powers of 10 together.
53 10 x10
3. Simplify within each group.
6
4. Combine the powers of ten.
1. Write problem.5310 x
810 x 6
What do you know about the size of
this number?
Example 4 Perform the indicated operation. Write the result in scientific notation.
64 10 x 610 x 4
2. Group the whole/decimal numbers together.
6 x 4
Group the powers of 10 together.
64 10 x10
3. Simplify within each group.
24
4. Write the whole/decimal number in scientific notation.
110 x 4.2
5. Combine the powers of ten.
10110 x 4.2
1. Write problem.6410 x
1010 x 24 1010 x
1110 x 4.2
What do you know about the size of
this number?
Example 5 Perform the indicated operation. Write the result in scientific notation.
48 10 x 810 x 1.7
2. Group the whole/decimal numbers together.
8 x .17
Group the powers of 10 together.
48 10 x10
3. Simplify within each group.
8.56
4. Write the whole/decimal number in scientific notation.
110 x 5.68
5. Combine the powers of ten.
4110 x 68.5
1. Write problem.4810 x
410 x 8.56 410 x
310 x 68.5
What do you know about the size of
this number?
Example 6 Perform the indicated operation. Write the result in scientific notation.
39 10 x 4.010 x 2.1
2. Group the whole/decimal numbers together.
0.4 x 2.1
Group the powers of 10 together.
39 10 x10
3. Simplify within each group.
48.0
4. Write the whole/decimal number in scientific notation.
110 x 8.4
5. Combine the powers of ten.
6110 x 8.4
1. Write problem. 3910 x
610 x 48.0 610 x
510 x 8.4
What do you know about the size of
this number?
Example 7 Perform the indicated operation. Write the result in scientific notation.
24 10 x .8510 x .52
2. Group the whole/decimal numbers together.
5.8 x .52
Group the powers of 10 together.
24 10 x10
3. Simplify within each group.
50.14
4. Write the whole/decimal number in scientific notation.
110 x 45.1
5. Combine the powers of ten.
6110 x 45.1
1. Write problem.2410 x
610 x 50.14 610 x
710 x 45.1
What do you know about the size of
this number?
210 x
Example 8 Perform the indicated operation. Write the result in scientific notation.
3
5
10 x 2
10 x 6
2. Group the whole/decimal numbers together.
2 6
Group the powers of 10 together.
3
5
10
10
3. Simplify within each group.
3
1. Write problem.
What is left over and
where is it located?
Example 9 Perform the indicated operation. Write the result in scientific notation.
2
6
10 x 8
10 x 5
2. Group the whole/decimal numbers together.
85
Group the powers of 10 together.
2
6
10
10 x
3. Simplify within each group.
625.
4. Write the whole/decimal number in scientific notation.5. Combine the powers of ten.
110 x 25.6
1. Write problem.
410 x 410 x
310 x 25.6
Example 10 Perform the indicated operation. Write the result in scientific notation.
6
2
10 x 810 x 5
2. Group the whole/decimal numbers together.
85
Group the powers of 10 together.
6
2
1010 x
3. Simplify within each group.
625.
4. Write the whole/decimal number in scientific notation.
110 x 25.6
5. Combine the powers of ten.
4110 x 6.25
1. Write problem.
2
6
1010 x
410 x .625 410 x
310 x 6.25What do you know about the size of
this number?
Example 11 Perform the indicated operation. Write the result in scientific notation.
1. Write problem. 24-10 x 5
2. Use power of product property.
242 10 x5
3. Write the whole/decimal number in scientific notation.
110 x 2.5
4. Combine the powers of ten. -710 x 2.5
810 x 25 810 x
What do you know about the size of
this number?
Bonus Write one in scientific notation.
1 010 x 1
8-A4 Pages 472–473 # 20–46, Page 474 Quiz 2, # 1–10.
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