# A new apartment complex has 155,400 yd2 of rentable space (Assume 4 Sig Figs). At \$17.57 per ft2 per month, and a 70% occupancy rate, how much income will this building generate in a year? What is the answer if “70%” is 1 Sig Fig’s? or 2 Sig Fig’s ? What about if rate is 70.2% occupancy (i.e. 3 Sig Figs)? What is the importance of Significant Figures?

To calculate the income generated by the new apartment complex, we need to consider the rentable space, the rental rate, and the occupancy rate. The relevance of significant figures in this calculation will also be discussed.

First, let’s calculate the total rentable area in square feet. Given that the apartment complex has 155,400 yd2 of rentable space, we need to convert this to square feet. Since 1 yard is equal to 3 feet, we can convert the square yards to square feet using the conversion factor (3 ft/1 yd):

155,400 yd2 * (3 ft/1 yd)^2 = 1,398,600 ft2

Now, we need to calculate the income generated in a year. To do this, we multiply the total rentable area by the rental rate per square foot per month and then by 12 months:

Income = (Total rentable area) * (Rental rate per ft2 per month) * 12 months

With the given rental rate of \$17.57 per ft2 per month, the occupancy rate of 70%, and the total rentable area of 1,398,600 ft2, we can calculate the income generated in a year:

Income = (1,398,600 ft2) * (\$17.57/ft2/month) * 12 months

Income = \$29,189,943.60

Therefore, the building will generate an income of approximately \$29,189,943.60 in a year, assuming a 70% occupancy rate, and all calculations are rounded to four significant figures.

Now let’s explore the impact of different numbers of significant figures on the calculation. If the occupancy rate is given as 70% with only one significant figure (1 Sig Fig), we should carry the result of the calculation with only one significant figure:

Income = (1,398,600 ft2) * (\$17.57/ft2/month) * 12 months

Income ≈ \$3,000,000

In this case, the income generated will be approximately \$3,000,000 with one significant figure.

If the occupancy rate is given with two significant figures (2 Sig Figs), we should carry the result of the calculation with two significant figures:

Income ≈ \$29,000,000

In this case, the income generated will be approximately \$29,000,000 with two significant figures.

Now, let’s consider a different occupancy rate of 70.2% with three significant figures (3 Sig Figs):

Income ≈ \$29,300,000

In this case, the income generated will be approximately \$29,300,000 with three significant figures.

The importance of significant figures lies in the communication of the precision of a measured or calculated value. Significant figures indicate the number of digits that can be relied upon and carry meaning in a given value. By using the appropriate number of significant figures, we can ensure the accuracy and precision of our calculations.

In the case of the apartment complex income calculation, using too many or too few significant figures can lead to inaccurate or misleading results. Rounding the final answer to an appropriate number of significant figures helps to maintain the precision and significance of the input data and calculations. It is important to adhere to the correct number of significant figures based on the given data to ensure the accuracy of the final result.