How to Determine when Zeros are Counted as Significant Figures

2 Introduction The significance of a zero in a number may be ambiguous. Sometimes a zero in a number merely acts as a placeholder and the zero is not significant. The zero in 720 is an example of this. Other times a zero in a number may be significant, the zero in 720. is an example of this. The goal of this lesson is to explain the rules that govern when a zero in a number is significant.

3 1) Every non-zero digit is significant 24.7, 0.743, and 714 all have 3 significant figures. 2) Zeros in between non-zero digits are significant! 7003, 40.79, and all have 4 significant figures. Rules that Govern the Significance of a Zero

4 3) Zeros to the right of the decimal and left of non-zero digits are not significant and 0.42 both have 2 significant figures. 4) Zeros to the right of the decimal and at the end of a number are significant! 43.00, 1.010, and all have 4 significant figures.

5 5a) Zeros at the end of a number and to the left of a non-visible decimal point are not significant since they merely act as placeholders. 300 has 1 significant figure has 3 significant figures. 5b) However, if a decimal point is visible, then these zeros represent known measured values and they are significant has 3 significant figures has 4 significant figures 5c) To avoid ambiguity, it is best to express this type of number using scientific notation 300 = 3. x significant figure = 3.00 x significant figures.

Is the digit a zero? Yes No Is a decimal point visible? No Is the zero left of the decimal point? Is the zero at the end of the number? No Yes No Digit in question The digit is significant The digit is not significant The digit is significant Are there any non-zero digits to the left of the zero? Yes The digit is not significant Yes No Are there any non-zero digits to the right of the zero? No Yes Flowchart for Determining the Significance of a Digit

1203 = = = 30.0 = = = = 6.21 x 10 4 = How Many Significant Figures are in Each Number?

1203 =4 sig. figs =4 sig. figs =4 sig. figs =3 sig. figs =4 sig. figs =2 sig. figs =5 sig. figs x 10 4 =3 sig. figs. How Many Significant Figures are in Each Number?