Significant Figures

Significant Figure

A prescribed decimal place that determines the amount of rounding off to be done based on the precision of the measurement.

Rule #1

Non-zero numbers are always significant.

Rule #2

Any zeros between two significant digits are significant. (ex: 5004 has four sigs)

Rule #3

Zeros to the left of a non-zero digit (regular number) are never significant. (Ex: 0.00500 (three sig figs)

Rule #4

A final zero or trailing zeros in the decimal portion ONLY are significant. (ex: 0.00500)

How many significant digits are in 48,923?

5 significant figures and rule 1.

How many significant digits are in 8.1000?

5 significant figures and rules 1, 2, and 4.

How many significant digits are in 501.040?

6 significant figures and rules 1, 2, 3, and 4.

How many significant digits are in 10.0?

3 significant figures and rules 1, 3, and 4.

Addition and Subtraction rules.

When adding or subtracting numbers, count the number of decimal places to determine the number of significant figures.

Multiplication and Division rules.

When multiplying or dividing numbers, count the number of significant figures. The answer cannot contain more significant figures than the number being multiplied or divided.

Rounding #1

If the digit to be dropped is greater than 5, the last retained digit is increased by one. For example, 12.6 is rounded to 13.

Rounding #2

If the digit to be dropped is less than five, the last remaining digit is left as it is. For example, 12.4 is rounded to 12.

Rounding #3

If the digit to be dropped is 5, and if any digit following is not zero, the last remaining digit is increased by one. For example, 12.51 is rounded to 13.

Rounding #4

If the digit to be dropped is 5, and is followed only by zeroes, the last remaining digit is increased by one if odd, but is left if even. For example, 11.5 is rounded to 12. 12.5 is rounded to 12.

Adding and Subtracting cont.

Adding and subtracting - Only look at the decimal portion. Answer must match the lowest no. of decimals.

Multiplication and Division cont.

Look at the whole number. Answer must match least number of significant digits.

How many significant figures are in 0.0000055 g?

2 significant figures.

How many significant figures are in 16402 g?

5 significant figures.

How many significant figures are in 3.40 x 10(3) ml?

3 significant figures.

Round up, if...

The next digit is greater than five, the next digit is 5 and there is a non-zero digit after, or the next digit is 5 and the curent digit to be rounded is odd.

Round down, if...

The next digit is less than 5, or the next digit is 5 followed by only zero digits or not followed by any other digits and the current digit to be rounded is even.

37.76 + 3.907 + 226.4

268.1

319.15 - 32.614

286.54

(5.5)(3)

1.7 x 10(2)