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Algebra 1
Section 8.4
Scientific Notation
Numbers in scientific notation are written as c × 10n,where c is
a decimal number greater than or equal to 1, and less than 10.
Examples:
3.2 × 103
Decimal Form
1,000,000,000
1,000,000
1,000
10
1
0.1
0.001
0.000001
2.134 × 10 –8
Power of 10
109
106
103
101
100
10-1
10-3
10-6
7.2601 × 100
Name
One billion
One million
One thousand
Ten
One
One tenth
One thousandth
One millionth
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To change from scientific notation to decimal notation:
- move the decimal point the same number of places as the
exponent on the 10.
- if it is a positive exponent, move right
- if it is a negative exponent, move left
Examples:
3.24 × 103
= 3240 move decimal point to right 3 places
4.01 × 109
= 4,010,000,000
move decimal point to right 9 places
3.82 × 10 –3
= .00382 move decimal point to left 3 places
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Rewrite the scientific notation in decimal notation.
1. 1.09 × 106
= 1,090,000
2. 7.021 × 10 -5
= .00007021
move decimal point to right 6 places
move decimal point to left 5 places
3. 6.21 × 100
= 6.21 move decimal point 0 places
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To change from decimal notation to scientific notation:
- start with one number in front of decimal point
- count the number of places the decimal point was moved
and that will be the exponent on the 10
- if it was moved left the exponent will be positive
- if it was moved right the exponent will be negative
Examples:
450,000
= 4.5 × 105
909,900,000
= 9.099 × 108
0.321
= 3.21 × 10 -1
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Rewrite the decimal notation in scientific notation.
1. 850,000,000,000
= 8.5 × 1011
2. 0.000456
= 4.56 × 10 - 4
3. 1
= 1 × 100
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Evaluate the expression.
1. 6 × 10-2 · 3 × 104
= (6 · 3) × (10-2 · 104) regroup numbers
= 18 × 102 simplify
= 1800
2. 4 × 104 · 2 × 10-1
= (4 · 2) × (104 · 10-1)
= 8 × 103 simplify
= 8000
3. 9 × 10 –3 · 4 × 108
= (9 · 4) × (10-3 · 108)
= 36 × 105 simplify
= 3,600,000
regroup numbers
regroup numbers
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Algebra 1
Section 8.4
Assignment
Rewrite the scientific notation in decimal form.
1.) 2.345 × 108
2.) 9.4675 × 104
3.) 7.021 × 10 -5
4.) 4.73 × 100
7.) 0.008367
8.) 0.0875
Rewrite the decimal in scientific notation.
5.) 900,000,000
6.) 67.8
Evaluate the expression. Write the result in decimal form.
9.) 5 × 105 • 5 × 10 -5
10. 6 × 10 -3 • 7 × 10 – 4
11.) 8 × 104 • 10 × 10 -1
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