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Chapter 2: Problem 157

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

Short Answer

Expert verified
(a) \(74.8 \pm 0.1 \mathrm{~m}\) (b) \(0.0026 \pm 0.0001 \mathrm{~g}\) (c) \((1.250 \pm 0.010) \times 10^{3} \mathrm{~L}\) (d) \(18 \pm 1 \mathrm{~cm}\) (e) 18 pennies

Step by step solution

01

Calculate Uncertainty for (a)

For the measurement \(74.8\mathrm{~m}\), the least significant digit is in the tenths place. Thus, the uncertainty in this measurement is represented as ±0.1 m. The measurement with its uncertainty can be written as \(74.8 \pm 0.1 \mathrm{~m}\).
02

Calculate Uncertainty for (b)

For the measurement \(0.0026\mathrm{~g}\), the least significant digit is in the ten-thousandths place. Therefore, the uncertainty in this measurement is represented as ±0.0001 g. The measurement with its uncertainty can be written as \(0.0026 \pm 0.0001 \mathrm{~g}\).
03

Calculate Uncertainty for (c)

For the measurement \(1.250 \times 10^{3}\mathrm{~L}\), the least significant digit is in the hundredths place. Thus, the uncertainty in this measurement is represented as ±0.01 L. However, the measurement is expressed in scientific notation, so we should express the uncertainty in the same format. The measurement with its uncertainty can be written as \((1.250 \pm 0.010) \times 10^{3} \mathrm{~L}\).
04

Calculate Uncertainty for (d)

For the measurement \(18\mathrm{~cm}\), the least significant digit is in the ones place. Thus, the uncertainty in this measurement is represented as ±1 cm. The measurement with its uncertainty can be written as \(18 \pm 1 \mathrm{~cm}\).
05

Calculate Uncertainty for (e)

The uncertainty associated with counting something, such as 18 pennies, is not due to the measuring instrument. Instead, this is a discrete counting measurement with no uncertainty, since we're sure of the number of pennies counted. Therefore, the measurement can be written as 18 pennies with no associated uncertainty.

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Most popular questions from this chapter

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