1.5 Measurement Uncertainty, Accuracy, and Precision

Express each of the following numbers in exponential notation with correct significant figures:

(a) 704

(b) 0.03344

(c) 547.9

(d) 22086

(e) 1000.00

(f) 0.0000000651

(g) 0.007157

Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:

(a) the number of seconds in an hour

(b) the number of pages in this book

(c) the number of grams in your weight

(d) the number of grams in 3 kilograms

(e) the volume of water you drink in one day

(f) the distance from San Francisco to Kansas City

How many significant figures are contained in each of the following measurements?

(a) 53 cm

(b) 2.05 $\times$ 10⁸ m

(c) 86,002 J

(d) 9.740 $\times$ 10⁴ m/s

(e) 10.0613 m³

(f) 0.17 g/mL

(g) 0.88400 s

Round off each of the following numbers to two significant figures:

(a) 0.436

(b) 9.000

(c) 27.2

(d) 135

(e) 1.497 $\times$ 10⁻³

(f) 0.445

Perform the following calculations and report each answer with the correct number of significant figures.

(a) 628 $\times$ 342

(b) (5.63 $\times$ 10²) $\times$ (7.4 $\times$ 10³)

(c) $\frac{28.0}{13.483}$

(d) 8119 $\times$ 0.000023

(e) 14.98 + 27,340 + 84.7593

(f) 42.7 + 0.259