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Chapter 1: Problem 26

A listing of a house for sale states that there are 5 bedrooms, \(4000 \mathrm{ft}^{2}\) of living area, and a living room with dimensions \(17 \times 18.5 \mathrm{ft}\). How many significant figures are there in each quantity? (Your answer may include the words ambiguous and exact.)

Short Answer

Expert verified
Based on the given information, determine the number of significant figures for each of the following quantities: the number of bedrooms, the living area in square feet, and the living room dimensions in feet. Answer: 1. Number of bedrooms: 1 significant figure. 2. Living area: 1 significant figure. 3. Living room dimensions: 2 significant figures for 17 ft and 3 significant figures for 18.5 ft.

Step by step solution

01

Determine significance of the number of bedrooms

There are 5 bedrooms mentioned in the listing. Since this is an integer, it would typically be considered to have an exact value, as it's not a measurement with potential variability. Number of bedrooms has 1 significant figure.
02

Determine significance of the living area

The living area is given as \(4000 \mathrm{ft}^{2}\). Since there are no decimals, we count the number of non-zero significant digits. In this case, there is only one significant figure, which is the 4 in 4000. However, this number might be ambiguous because it could have been rounded down, and the exact value might contain more significant figures. Without further information, we cannot assume additional significant figures.
03

Determine significance of living room dimensions

The dimensions of the living room are given as \(17 \times 18.5 \mathrm{ft}\). In this case, both numbers are significant since they include a decimal point, and we count all the digits. The dimension 17 has an exact value, so it would have 2 significant figures. The other dimension, 18.5, has a decimal, so every digit is significant, giving it 3 significant figures in total. To summarize: 1. Number of bedrooms: 1 significant figure (exact). 2. Living area: 1 significant figure (ambiguous). 3. Living room dimensions: 2 significant figures for 17 (exact) and 3 significant figures for 18.5.

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