RULES FOR USING SIGNIFICANT FIGURES



RULES FOR USING SIGNIFICANT FIGURES

1. All non zero digits are significant. Examples: 256 (3); 13.51 (4)

2. Captive zeros(zeros between two non zero digits) are always significant. Examples: 3008 (4); 10.5 (3); 27.004 (5)

3. Trailing zeros (zeros to the right of a non zero digit) are significant when a decimal point is visible somewhere in the number. Trailing zeros that act as placeholders for an understood decimal point are never significant. Examples: 28.400 (5); 1.0 (2); 900. (3); 900 (1); 260.0 (4)

4. Leading zeros (zeros before a non zero digit) are never significant. Examples: 0.0076 (2); 0.020(2); 0.456 (3)

5. Exact or counted numbers have an infinite number of significant figures. Examples: 8 cars; metric equalities ( 1m = 1000mm)

RULES FOR CALCULATING WITH SIGNIFICANT FIGURES

1. Addition and Subtraction: the answer is rounded to match the number with the fewest decimal places in the addition or subtraction problem.

Examples: 677 + 39.2 + 6.23 = 722.43 = rounded to 722 because 677 does not have any digits to the right of the decimal.

21.277 – 10.8 = 10.477 = rounded to 10.5 because 10.8 only has 1 digit to the right of the decimal.

2. Multiplication and Division: the answer is rounded to match the number with the least number of significant figures in the multiplication or division problem.

Examples: 1.1330 x 5.126 = 5.807758 = rounded to 5.808

(5) (4) (7) (4)

140.8 / 20.1 = 7.004975124 = rounded to 7.00

(4) (3) (10) (3)

RULES FOR ROUNDING NUMBERS

1. Determine the number of significant figures needed.

2. Move one place to the right.

a. if that number is less than 5, the previous number remains the same.

b. if that number is 5 or greater, round the previous number up 1.

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