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# Scientific Notation

Scientific Notation. Scientific Notation. Scientist need to express either very small numbers or very large number * the mass of a proton in a Hydrogen atom 0.000 000 000 000 000 000 000 000 001 673kg A single gram of Hydrogen has 602 000 000 000 000 000 000 000 H atoms.

## Scientific Notation

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1. Scientific Notation

2. Scientific Notation • Scientist need to express either very small numbers or very large number * the mass of a proton in a Hydrogen atom • 0.000 000 000 000 000 000 000 000 001 673kg • A single gram of Hydrogen has 602 000 000 000 000 000 000 000 H atoms

3. Scientific Notation • To easily express the numeric value of large and small numbers we use scientific notation. • Def: an expression of numbers in the form m x 10n, where m is equal to or greater than 1 and less than 10, and n is an integer.

4. Scientific Notation • Scientific notation has 2 parts. m x 10 n • A coefficient – a number in which one digit is placed to the left of the decimal. • An exponent – a power of 10 by which the number is multiplied.

5. Positive exponent • A positive exponent indicates the number of times the coefficient must be multiplied by 10. • Each time the decimal place is moved one place to the left, the exponent is increased by one.

6. Express 1234.56 in scientific notation 1234.56 x 100 123.456 x 101 12.3456 x 102 1.23456 x103

7. Negative exponents • A negative exponent indicates the number of times a coefficient must be divided by 10. • Each time the decimal place is moved one place to the right, the exponent is decreased by one.

8. Express 0.006 57 in scientific notation • 0.006 57 x 100 • 0.0657 x 10-1 • 0.657 x 10-2 • 6.57 x 10-3

9. Express the following in scientific notation • 230 • 2.3x102

10. Express the following in scientific notation • 5601 • 5.601 x103

11. Express the following in scientific notation • 14 100 000 • 1.41 x 107

12. Express the following in scientific notation • 56 million • 5.6 x 107

13. Express the following in scientific notation • 0.450 13 • 4.5013 x 10-1

14. Express the following in scientific notation • 0.089 • 8.9 x 10-2

15. Express the following in scientific notation • 0.000 26 • 2.6 x 10-4

16. Express the following in scientific notation • 0.000 000 698 • 6.98 x 10-7

17. Express the following in scientific notation • 12 thousandth • 1.2 x 10-2

18. Express the following in scientific notation • The speed of light in a vacuum is 299 792 458 m/s * 2.997 924 58 x 108 m/s

19. Express the following in scientific notation • The mean radius of Earth is 6 378km * 6.378 x 103km

20. Express the following in scientific notation • The density of Oxygen is 0.001 42 g/ml * 1.42 x 10-3g/ml

21. Express the following in scientific notation • The radius of an Argon atom is 0.000 000 000 098m • 9.8 x 10-11m

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