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Chapter 2: Problem 63

What is the uncertainty in each measured number: (a) \(12.60 \mathrm{~cm}\) (b) \(12.6 \mathrm{~cm}\) (c) \(0.00000003\) in. (d) \(125 \mathrm{ft}\)

Short Answer

Expert verified
The uncertainties for the given measurements are: (a) \(12.60 \pm 0.01 \mathrm{~cm}\) (b) \(12.6 \pm 0.1 \mathrm{~cm}\) (c) \(0.00000003 \pm 0.00000001 \mathrm{~in}\) (d) \(125 \pm 1 \mathrm{~ft}\)

Step by step solution

01

a) Finding uncertainty for 12.60 cm

In this measurement, the smallest division (least count) is given up to two decimal places (hundredth of a centimeter). Therefore, the uncertainty for this measurement is ± 0.01 cm. The measurement with uncertainty will be expressed as \(12.60 \pm 0.01 \mathrm{~cm}\).
02

b) Finding uncertainty for 12.6 cm

In this measurement, the smallest division (least count) is given up to one decimal place (tenth of a centimeter). Therefore, the uncertainty for this measurement is ± 0.1 cm. The measurement with uncertainty will be expressed as \(12.6 \pm 0.1 \mathrm{~cm}\).
03

c) Finding uncertainty for 0.00000003 in

In this measurement, the smallest division (least count) is given up to 8 decimal places. Therefore, the uncertainty for this measurement is ± 0.00000001 in. The measurement with uncertainty will be expressed as \(0.00000003 \pm 0.00000001 \mathrm{~in}\).
04

d) Finding uncertainty for 125 ft

In this measurement, the smallest division (least count) is given as 1 ft (no decimals). Therefore, the uncertainty for this measurement is ± 1 ft. The measurement with uncertainty will be expressed as \(125 \pm 1 \mathrm{~ft}\).

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Most popular questions from this chapter

True or false? If any statement is false, rewrite it to make it true. (a) When multiplying or dividing a series of measured values, the number of significant figures in the answer is determined by the measured value having the fewest significant figures. (b) When adding or subtracting a series of measured values, the number of significant figures in the answer is determined by the measured value having the fewest significant figures.

A student takes three measurements of the mass of an object. If the actual mass is \(8.54 \mathrm{~g}\), indicate whether each set of measurements is precise but not accurate, accurate but not precise, both accurate and precise, or neither accurate nor precise: (a) \(6.38 \mathrm{~g}, 9.23 \mathrm{~g}, 4.36 \mathrm{~g}\) (b) \(8.53 \mathrm{~g}, 8.59 \mathrm{~g}, 8.55 \mathrm{~g}\) (c) \(9.53 \mathrm{~g}, 8.54 \mathrm{~g}, 7.54 \mathrm{~g}\) (d) \(6.25 \mathrm{~g}, 6.27 \mathrm{~g}, 6.26 \mathrm{~g}\)

Convert: (a) \(7.98 \times 10^{23} \mu \mathrm{L}\) to liters (b) \(3.00 \times 10^{-3} \mathrm{mg}\) to grams (c) \(4.21 \times 10^{8} \mathrm{~mL}\) to gallons \(\left[1 \mathrm{~m}^{3}=264\right.\) gallons \(]\)

Indicate the uncertainty in: (a) \(74.8 \mathrm{~m}\) (b) \(0.0026 \mathrm{~g}\) (c) \(1.250 \times 10^{3} \mathrm{~L}\) (d) \(18 \mathrm{~cm}\) (e) 18 pennies

Using a bathroom scale, a tub, a sponge, and a measuring cup, explain how you would measure your own density.
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