Question

practice problems

1. how many significant figures are in each of the following?

a) 3.405
b) 0.00289
c) 1030
d) 7.0040 x 10^3
e) 102.00
f) 0.000960
g) 9.80

1. perform the following calculations to the correct number of significant figures

a) 12.0550 + 9.05
b) 257.2 - 19.769
c) (6.21 x 10^7)(0.150)
d) 0.0577 + 0.753
e) 27.5 x 1.82 + 100.04
f) (2.290 x 10^4)+(6.7 x 10^3)
g) (26.7 x 10^4)+48.533+144.99

1. round each of the following numbers to three significant figures:

a) 342.79513
b) 9.845.8749
c) 0.0000045389
d) 2.45555567
e) 76.89
f) 56.9971

Explanation:

Step1: Recall significant - figure rules

Non - zero digits are always significant. Zeros between non - zero digits are significant. Leading zeros are not significant. Trailing zeros are significant if there is a decimal point.

Step2: Determine significant figures in part a

For 3.405, non - zero digits 3, 4, 5 and the zero between 4 and 5 are significant. So there are 4 significant figures.

Step3: Determine significant figures in part b

For 0.00289, leading zeros are not significant. So there are 3 significant figures (2, 8, 9).

Step4: Determine significant figures in part c

For 1030, trailing zeros without a decimal point are not significant. So there are 3 significant figures (1, 0, 3).

Step5: Determine significant figures in part d

For \(7.0040\times10^{3}\), in scientific notation, all digits in the coefficient are significant. So there are 5 significant figures (7, 0, 0, 4, 0).

Step6: Determine significant figures in part e

For 102.00, non - zero digits and trailing zeros with a decimal point are significant. So there are 5 significant figures (1, 0, 2, 0, 0).

Step7: Determine significant figures in part f

For 0.000960, leading zeros are not significant, and the trailing zero after 96 is significant. So there are 3 significant figures (9, 6, 0).

Step8: Determine significant figures in part g

For 9.80, non - zero digits and the trailing zero with a decimal point are significant. So there are 3 significant figures (9, 8, 0).

Answer:

a) 4
b) 3
c) 3
d) 5
e) 5
f) 3
g) 3