Question

A basketball game at the University of Connecticut's Gampel Pavilion attracted 10,000 people. The building's interior floor space has an area of \(1.71 \times 10^{5} \mathrm{ft}^{2} .\) Tickets to the game sold for \(\$ 22.00 .\) Senior citizens were given a \(20 \%\) discount. How many significant figures are there in each quantity? (Your answer may include the words ambiguous and exact.

Short answer

Answer: The number of significant figures in each quantity are as follows: 10,000 people - 1 significant figure, 1.71 x 10^5 ft² - 3 significant figures, $22.00 ticket price - 4 significant figures, and the 20% senior citizen discount is ambiguous as it can be considered an exact value.

Step-by-step solution

1. Number of Significant Figures in 10,000

For 10,000, there are only one significant figure (1). The zeros are placeholders and do not count as significant figures.

2. Number of Significant Figures in 1.71 x 10^5 ft²

In the scientific notation form (1.71 x 10^5), there are three significant figures, which are 1, 7, and 1. The exponent in the scientific notation does not affect the significant figures.

3. Number of Significant Figures in \(22.00

For \)22.00, all digits (2, 2, 0, 0) are considered significant, since they explicitly represent the exact amount. Therefore, there are 4 significant figures.

4. Number of Significant Figures in 20% Discount

For 20%, the value is considered an exact value since it is a predefined discount rate. However, if we consider it as a number and convert it to decimal form (0.20), it would have 2 significant figures. But given the context, it can be considered ambiguous, as it is more appropriate to view it as an exact value. In summary: 1. 10,000: 1 significant figure 2. 1.71 x 10^5 ft²: 3 significant figures 3. $22.00: 4 significant figures 4. 20% discount: ambiguous (exact)