Significant Figures

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RULES:

1. All non-zero numbers ARE significant. The number 33.2 has THREE significant figures

2. Zeros between two non-zero digits ARE significant. 2051 has FOUR significant figures.

3. Leading zeros are NOT significant. The number 0.0032 has only TWO significant figures.

4. Trailing zeros to the right of the decimal ARE significant. There are FOUR significant figures in 92.00.

5. Trailing zeros in a whole number with the decimal shown ARE significant. 540. there are THREE significant figures in this value.

6. Trailing zeros in a whole number with no decimal shown are NOT significant. 540 are only TWO significant figures in this value.

7. Exact numbers have an INFINITE number of significant figures.

8. For a number in scientific notation: N x 10x, all digits comprising N ARE significant by the first 6 rules; "10" and "x" are NOT significant. 5.02 x 104 has THREE significant figures

To make sure that the awnser you get isn't more precise than the numbers you started with. Significant figures are useful because they tell us how to round.

You round the number that has the less sinificant figures . Like 524 has 3 significant digits and 22 has 2 significant digits, the awnser of 524 * 22 = 11 528. So you round only two numbers, the round would be = 12 000and the rest you make them zeros.

Zeros that are sandwiched between none-zero are always significant.

Example: 3, 091 has 4 significant figures because thezero is between to none-zero numbers.

5.00603 = 6 significant figures

Zeros that come before all none-zero digits are never significat.

Example: 0.000491 only 3 significant figures because the zeros come before the digits.

Zeros that come after nonzero digits:

83 000 = 2 sf

83 000. = 5 sf

83.000 = 5 sf

Density= mas/volume

62 / 41 = 1.512195122

2 sf 2 sf 1.5

Number that have different amount of significant figures:

62 881 / 97 = 648.257732

5 sf 2 sf 650.00

5 621 * 3 = 5 019 553

4 sf 1 sf 5 020 000

218 / 26 = 8.386154

3 sf 2 sf 8.4

59 411 *2 = 118 822

5 sf 1 sf 100 000

Practice Problems:

10082 = 5 sf

70 000 000 = 1 sf

70 000 000. = 8 sf

0.0025 = 2 sf

0.00008914 = 4 sf

84.1000 = 7 sf

3 008 000 = 4 sf

0.000339 = 3 sf

0052305000000 = 5 sf

005230.5000000 = 11 sf

0.052305000000 = 11 sf

5.3 X 10+2 = 2 sf

5.30 X 10+2 = 3 sf

0.0530 X 10+2 = 3 sf