Question

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

Answer: The number of bedrooms has an exact number of significant figures (no uncertain digits), the living area has 4 significant figures, and the dimensions of the living room have 2 and 3 significant figures, respectively.

Step-by-step solution

Number of Bedrooms

There are 5 bedrooms in the house. Since this number is an exact count (whole number) and not a measured value, we consider it to be an exact quantity. Therefore, there are no uncertain digits in the number of bedrooms.

Living Area

The living area of the house is given as \(4000 \mathrm{ft}^{2}\). In this case, the last digit (zero) is uncertain and we consider it as a significant figure along with the other digits (4, 0, and 0). So, the living area has 4 significant figures.

Dimensions of Living Room

The living room has dimensions of \(17 \times 18.5 \mathrm{ft}\). These dimensions are measured values. The number "17" has two significant figures (1 and 7), as both digits are certain. The number "18.5" contains three significant figures: the first two digits (1 and 8) are certain, while the last digit (5) could be uncertain. Therefore, the dimensions of the living room have 2 and 3 significant figures, respectively. In conclusion, there are: - An exact number of significant figures in the number of bedrooms (no uncertain digits) - 4 significant figures in the living area - 2 and 3 significant figures in the dimensions of the living room.