Question

practice problems

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

a) 0.00452
b) 5.070
c) 4,800 (no decimal shown)
d) 4.800×10³

1. perform the following calculations and report the answer with the correct number of significant figures:

a) 3.45×2.1 =
b) 4.560 + 1.4 =
c) (5.22×10³)÷(2.1×10²) =

Explanation:

1. Determine significant - figures:

a) 0.00452

Leading zeros are not significant. So, the significant figures are 4, 5, 2. The number of significant figures is 3.

b) 5.070

All non - zero digits and zeros between non - zero digits and trailing zeros after a decimal point are significant. So, the significant figures are 5, 0, 7, 0. The number of significant figures is 4.

c) 4,800 (no decimal shown)

Trailing zeros without a decimal point are not significant. So, the significant figures are 4, 8. The number of significant figures is 2.

d) 4.800×10³

In scientific notation, all digits in the coefficient are significant. So, the significant figures are 4, 8, 0, 0. The number of significant figures is 4.

2. Perform calculations and determine significant - figures:

a) 3.45×2.1

First, calculate the product: 3.45×2.1 = 7.245. For multiplication, the answer has the same number of significant figures as the factor with the fewest significant figures. 2.1 has 2 significant figures. Rounding 7.245 to 2 significant figures gives 7.2.

b) 4.560 + 1.4

First, perform the addition: 4.560+1.4 = 5.960. For addition, the answer has the same number of decimal places as the number with the fewest decimal places. 1.4 has 1 decimal place. Rounding 5.960 to 1 decimal place gives 6.0.

c) (5.22×10³)÷(2.1×10²)

First, perform the division of the coefficients: $\frac{5.22}{2.1}=2.485714\cdots$ and subtract the exponents of 10: $10^{3 - 2}=10^{1}$. So the result is 2.485714⋯×10¹. 2.1 has 2 significant figures. Rounding 2.485714⋯×10¹ to 2 significant figures gives 2.5×10¹.

Answer:

1.
a) 3
b) 4
c) 2
d) 4
2.
a) 7.2
b) 6.0
c) 2.5×10¹