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Chapter 1: Problem 108

List the following in the order of increasing precision, indicating any quantities about which the precision is uncertain: (a) \(1400 \mathrm{km} ;\) (b) \(1516 \mathrm{kg} ;\) (c) \(0.00304 \mathrm{g};\) (d) \(125.34 \mathrm{cm} ;\) (e) \(2000 \mathrm{mg}\).

Short Answer

Expert verified
The measurements ranked in order of increasing precision are: 1400 km, 1516 kg, 2000 mg, 125.34 cm, and 0.00304 g. The precision remains uncertain for 1400 km and 2000 mg because they end with zero.

Step by step solution

01

Understand the Concept of Precision

Precision in measurements refers to the smallest possible unit or increment. A measurement with a smaller unit is considered more precise.
02

Identify Precision for Each Quantity

In order to rank the quantities, one must look at each given measure and identify its degree of precision. Here are the identified levels: (a) 1400 km is precise to the nearest 100 km, (b) 1516 kg is precise to the nearest 1 kg, (c) 0.00304 g is precise to the nearest 0.00001 g, (d) 125.34 cm is precise to the nearest 0.01 cm, and (e) 2000 mg is precise to the nearest 1 mg.
03

Understand Uncertainty in Measurements

Uncertainty generally arises when a measure ends with 0. It is unclear whether that zero is a part of a precise measurement or it was put on approximated basis. In this set, (a) 1400 km and (e) 2000 mg have an uncertainty because they end with zero.
04

Organise the Measures in Order of Increasing Precision

After identifying the degree of precision for each, they can be ordered from the least precise to the most: (a) 1400 km, (b) 1516 kg, (e) 2000 mg, (d) 125.34 cm, and (c) 0.00304 g. This order represents increasing precision.

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