Scientific Notation and Significant Digits

In scientific notation, a number has the form a × 10 n , eh times , 10 to the n , comma where n is an integer and 1 ≤ a < 10 . 1 less than or equal to eh less than 10 .

Example 1

Write 5 . 59 × 10 6 5 . 59 times , 10 to the sixth in standard form.

Example 2

Write 0.0000318 in scientific notation.

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.

Example 3

Multiply ( 6 . 71 × 10 8  mi  / h )  and  ( 3 . 8 × 10 4 h ) . open 6 . 71 times , 10 to the eighth , mi , slash h close , and , open 3 . 8 times , 10 to the fourth , h close .

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Exercises

Change each number to scientific notation or to standard form.

1. 1,340,000
2. 6 . 88 × 10 − 2 6 . 88 times , 10 super negative 2 end super
3. 0.000775
4. 0.0072
5. 1 . 113 × 10 5 1 . 113 times , 10 to the fifth
6. 8 . 0 × 10 − 4 8 . 0 times , 10 super negative 4 end super
7. 1895
8. 2 . 3 × 10 3 2 . 3 times , 10 cubed
9. 123,400
10. 7 . 985 × 10 4 7 . 985 times , 10 to the fourth

Write each product or quotient in scientific notation. Round to the appropriate number of significant digits.

11. ( 1 . 6 × 10 2 ) ( 4 . 0 × 10 3 ) open 1 . 6 times , 10 squared , close open 4 . 0 times , 10 cubed , close
12. ( 2.5 × 10 − 3 ) ( 1 . 2 × 10 4 ) open 2.5 times , 10 super negative 3 end super , close open 1 . 2 times , 10 to the fourth , close
13. ( 4.237 × 10 4 ) ( 2.01 × 10 − 2 ) open , 4.237 , times , 10 to the fourth , close open , 2.01 , times , 10 super negative 2 end super , close
14. 7.0 × 10 5 2.89 × 10 3 fraction 7.0 times , 10 to the fifth , over 2.89 , times , 10 cubed end fraction
15. 1.4 × 10 4 8.0 × 10 2 fraction 1.4 times , 10 to the fourth , over 8.0 times , 10 squared end fraction
16. 6.48 × 10 6 3.2 × 10 5 fraction 6.48 , times , 10 to the sixth , over 3.2 times , 10 to the fifth end fraction
17. ( 1 . 78 × 10 − 7 ) ( 5 . 03 × 10 − 5 ) open 1 . 78 times , 10 super negative 7 end super , close open 5 . 03 times , 10 super negative 5 end super , close
18. ( 7 . 2 × 10 11 ) ( 5 × 10 6 ) open 7 . 2 times , 10 to the eleventh , close open 5 times , 10 to the sixth , close
19. ( 8 . 90 × 10 8 ) ÷ ( 2 . 36 × 10 − 2 ) open 8 . 90 times , 10 to the eighth , close divides open 2 . 36 times , 10 super negative 2 end super , close
20. ( 3 . 95 × 10 4 ) ÷ ( 6 . 8 × 10 8 ) open 3 . 95 times , 10 to the fourth , close divides open 6 . 8 times , 10 to the eighth , close
21. ( 4 . 9 × 10 − 8 ) ÷ ( 2 . 7 × 10 − 2 ) open 4 . 9 times , 10 super negative 8 end super , close divides open 2 . 7 times , 10 super negative 2 end super , close
22. ( 3 . 972 × 10 − 5 ) ( 4 . 7 × 10 − 4 ) open 3 . 972 times , 10 super negative 5 end super , close open 4 . 7 times , 10 super negative 4 end super , close

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