Sc i e n t i f i c N o t a t i o n a n d Si g n i f i c a n t D i g i t s
In scientific notation, a n u m b e r h as th e form a X 10” , w here n is an integer
and 1 < I a I < 10.Ex a m p l e 1
Write 5.59 x 106 in standard form.
I t
5.59 X 106 = 5 590 000 = 5,590,000 A positive exponent indicates a value greater than 1.
Move the decimal po in t six places to the right.Ex a m p l e 2
Write 0.0000318 in scientific notation.
0.0000318 = 3.18 X 10 5
I *Move the decimal p o in t to create a number between 1 and 10.
Since the original number is less than 1, use a negative exponent.W hen a m easu rem en t is in scientific notation, all th e digits of th e n u m b e r betw een
1 an d 10 are significant digits. W hen you m ultiply or divide m easu rem en ts, your
answ er should have as m any significant digits as th e least n u m b e r of significant
digits in any of the n u m b ers involved.
Ex a m p l e 3
Multiply (6.71 x 108 m i/h ) and (3.8 x 104 h).
(6.71 X 108 mi/h)(3.8 X 104 h) = (6.71 • 3.8)(10 8 • 104)
t = 25.498 X 1012
three tw o , ,
significant significant ~ 2 5 4 9 8 x 10
digits digits «= 2.5 X 1013m iRearrange factors.
Add exponents w hen m ultiplying powers o f 10.
W rite in scientific notation.
Round to tw o significant digits.Ex e r c i se s
Change each num ber to scientific notation or to standard form.
1. 1,340,000 2. 6.88 X 10 -2 3. 0.000775
6. 8.0 X 10 “4 7. 1895 8. 2.3 X 1034. 0.0072
9. 123,4005. 1.113 X 105
10. 7.985 X 104Write each product or quotient in scientific notation. Round to the appropriate
num ber of significant digits.
11. (1.6 X 102 )(4.0 X 103)
14. 7.0 X 10^5
2.89 X 10d
17. (1.78 X 10_7)(5.03 X 10~5)
20. (3.95 X 104) = (6.8 X 108)12. (2.5 X 10_ 3 )(1.2 X 104)
15 .1.4 X 10^4
8.0 X 10 2
18. (7.2 X 1011)(5 X 106)
21. (4.9 X 10- 8 ) - (2.7 X 10- 2 )- (4.237 X 104 )(2.01 X 10- 2 )
1g 6.48 X 10 6
3.2 X 10 5
19. (8.90 X 108) -h (2.36 X 10~2) - (3.972 X 10_ s )(4.7 X 10” 4)
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