Download Scientific Notation and Significant Digits

Scientific Notation and Significant Digits
In scientific notation, a number has the form a 3 10 n, where n is an integer and
1 # a , 10.
1
EXAMPLE
Write 5.59 3 10 6 in standard form.
5.59 3 10 6 = 5 590 000
A positive exponent indicates a value greater than 1.
Move the decimal point six places to the right.
= 5, 590, 000
2
EXAMPLE
Write 0.000 031 8 in scientific notation.
0.0000318 = 3.18 3 10-5
Move the decimal point to create a number between 1
and 10 (five places to the right). Since the original
number is less than 1, use a negative exponent.
When a measurement is in scientific notation, all the digits of the number between
1 and 10 are significant digits. When you multiply or divide measurements, your
answer should have as many significant digits as the least number of significant
digits in any of the numbers involved.
3
EXAMPLE
Multiply A 6.71 3 108 mi/h B and A 3.8 3 104 h B .
A 6.71 3 10 8 mi/h B A 3.8 3 10 4 h B =
=
=
<
three
significant
digits
4
two
significant
digits
EXAMPLE
10 5
22
6.332 3
1.6 3 10
(6.71 ? 3.8)(10 8 ? 10 4 B
25.498 3 10 12
2.5498 3 10 13
2.5 3 10 13 mi
Rearrange factors.
Add exponents when multiplying powers of 10.
Write in scientific notation.
Round to two significant digits.
5
Simplify 6.332 3 10
22 .
1.6 3 10
5 - (-2)
= 6.332
1.6 3 10
Subtract exponents when dividing powers of 10.
= 3.9575 3 10 7
< 4.0 3 10 7
Simplify.
Round to two significant digits.
EXERCISES
Change each number to scientific notation or to standard form. 1–10. See margin.
1. 1,340,000
2. 6.88 3 10-2
3. 0.000775
4. 0.0072
5. 1.113 3 10 5
6. 8.0 3 10-4
7. 1895
8. 2.3 3 10 3
9. 123,400
10. 7.985 3 10 4
Write each product or quotient in scientific notation. Round to the appropriate
number of significant digits. 11–22. See margin.
11. A 1.6 3 10 2 B A 4.0 3 10 3 B
5
14. 7.0 3 10 3
2.89 3 10
17. A 1.78 3
10 -7 B A 5.03
3
10 -5 B
20. A 3.95 3 10 4 B 4 A 6.8 3 10 8 B
854
Skills Handbook
12. A 2.5 3 10 -3 B A 1.2 3 10 4 B
4
15. 1.4 3 10 2
8.0 3 10
18. A 7.2 3
10 11 B A 5
3
10 6 B
21. A 4.9 3 10 -8 B 4 A 2.7 3 10 -2 B
13. A 4.237 3 10 4 B A 2.01 3 10 -2 B
6
16. 6.48 3 105
3.2 3 10
19. A 8.90 3 10 8 B 4 A 2.36 3 10 -2 B
22. A 3.972 3 10 -5 B A 4.7 3 10 -4 B