Significant FiguresSignificant Figures

Used to report all precisely known Used to report all precisely known numbers + one estimated digitnumbers + one estimated digit

Rule #1Rule #1

Every nonzero digit is significantEvery nonzero digit is significant

Examples:Examples:

24 = 224 = 2

3.56 = 33.56 = 3

7 = 17 = 1

Rule #2Rule #2

Zeros between non-zeros are significantZeros between non-zeros are significant

Examples:Examples:

7003 = 47003 = 4

40.9 = 3 40.9 = 3

Rule #3Rule #3

Zeros appearing in front of non-zero digits Zeros appearing in front of non-zero digits are are notnot significant significant

Act as placeholdersAct as placeholdersCan’t be dropped, show magnitudeCan’t be dropped, show magnitude

Examples:Examples:

0.00024 = 20.00024 = 2

0.453 = 30.453 = 3

Rule #4Rule #4

Zeros at the end of a number Zeros at the end of a number andand to the to the right of a decimal point are significant.right of a decimal point are significant.

Examples:Examples:

43.00 = 443.00 = 4

1.010 = 41.010 = 4

1.50 = 31.50 = 3

Rule #5Rule #5

Zeros at the end of a number Zeros at the end of a number when no decimal point decimal point is present aren’t significant.

Examples:Examples:

300 = 1300 = 1

27,300 = 327,300 = 3

Special RuleSpecial RuleAlways remember PAAlways remember PA

P A

If a decimal point is present, start on the Pacific (P) side and begin counting at the first non-zero digit all the way to the end.

If a decimal is absent, start on the Atlantic (A) side and begin counting at the first non-zero digit all the way to the end.

Special Rule (cont.)Special Rule (cont.)

Remember PARemember PA

Examples:Examples:

123.003 = decimal present, 123.003 = decimal present, start on “P” side, begin countingstart on “P” side, begin counting

Answer = 6Answer = 6

Special Rule (cont.)Special Rule (cont.)

Remember PARemember PA

Examples:Examples:204,000 = decimal absent, start 204,000 = decimal absent, start

on “A” side, begin counting at first non-on “A” side, begin counting at first non-zero digit until you hit the end of the zero digit until you hit the end of the number.number.

Answer = 3Answer = 3

Sig. Fig. Math RulesSig. Fig. Math Rules

Multiplication / Division:Multiplication / Division:

Your answer can’t have more sig. figs. Your answer can’t have more sig. figs. than the number in the problem with the than the number in the problem with the least amt. of sig. figs.least amt. of sig. figs.

Example = 60.56227892 x 35.25Example = 60.56227892 x 35.25

Calculator says – 2134.890832 (wrong)Calculator says – 2134.890832 (wrong)

Answer - 2135 Answer - 2135

Sig. Fig. Math RulesSig. Fig. Math Rules

Addition / Subtraction:Addition / Subtraction:Answers can’t have more numbers to Answers can’t have more numbers to

the right of the decimal point than the the right of the decimal point than the number in the problem with the least amt. number in the problem with the least amt. of numbers to the right of the decimal of numbers to the right of the decimal point.point.

Example = 24.1 + 3.35 + 2.23Example = 24.1 + 3.35 + 2.23Calculator says – 29.68 (wrong)Calculator says – 29.68 (wrong)Answer – 29.7Answer – 29.7