Question

It is often useful to use benchmark percents to estimate the values of actual percents. Useful benchmarks include multiples of \(10 \%\) ( \(10 \%\), \(20 \%, 30 \%, \text { and so on }),\) as well as \(25 \%\) and \(75 \%\) a. Of the 910 students attending Mill Middle School, 179 walk to school. Use a benchmark to estimate the percent of students who walk to school, and explain how you decided which benchmark to use. b. A human skeleton is made up of 206 bones. There are 54 bones in the hands. Use a benchmark to estimate the percent of a human skeleton's bones found in the hands, and explain how you decided which benchmark to use. c. The girl's softball team won 25 of the 33 games it played last season. Use a benchmark to estimate the percent of games the team won, and explain how you decided which benchmark to use.

Short answer

a. 20%. b. 25%. c. 75%.

Step-by-step solution

Estimate Percent of Students Walking to School

First, compute the actual percent of students walking by using the formula \(\text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100\). Plug in the values: \(\text{Percent} = \frac{179}{910} \times 100 \approx 19.67\text{\text{\thinspace\thinspace\thinspace}}\text{\text{\thinspace\thinspace}'}\). Use the closest benchmark, which in this case is 20%.

Estimate Percent of Bones in the Hands

First compute the actual percent of bones in the hands: \(\text{Percent} = \frac{54}{206} \times 100 \approx 26.21\text{\text{\thinspace\thinspace\thinspace}}\text{\text{\thinspace\thinspace}'}\). The closest benchmark is 25%.

Estimate Percent of Games Won

First, we compute the actual percent of games won: \(\text{Percent} = \frac{25}{33} \times 100 \approx 75.76\text{\text{\thinspace\thinspace\thinspace}}\text{\text{\thinspace\thinspace}'}\). Use the closest benchmark, which is 75%.

Key concepts

Estimating Percents

Estimating percents is a great technique to quickly understand and communicate approximate values. Instead of getting lost in precise calculations, we use simplified benchmarks to come to a close-enough figure.
For instance, if you see 179 out of 910 students walk to school, calculating the exact percentage might take time. But using estimation, you can quickly figure that 179 is about 20% of 910 by knowing 20% of anything is roughly a fifth.
This simplifies the problem and gives you a good enough approximation for most purposes, without needing a calculator.

Multiples of 10%

Multiples of 10% serve as easy-to-remember benchmarks when estimating percentages. These include 10%, 20%, 30%, up to 100%.
These benchmarks are universally useful since they're easy math markers and help in quick calculations.
To estimate the percent of bones in the hands out of a total skeleton, you can round up to the nearest multiple of 10%. For example, 54 out of 206 bones is close to 50 out of 200 bones, which is 25%.

Mathematical Estimation

Mathematical estimation involves using approximation techniques to come close to an exact number without needing full precision. This is helpful in everyday scenarios where making quick, reasonably accurate decisions is important.
When you estimate percent, you look at the value and choose the nearest easy-to-remember benchmark. For example, 25 games out of 33 won by a team is just above 75%. So, rounding to 75% gives you a quick and fairly accurate estimate.

Percentage Calculation

Calculating percentages involves using the formula: ewline \[ \text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100 \] ewline This formula converts a fraction or proportion into a percentage.
For instance, to calculate the exact percentage of students walking to school, you would use: ewline \[ \text{Percent} = \frac{179}{910} \times 100 \] ewline Doing this gives approximately 19.67%, but for practical purposes, we can approximate it to the closest benchmark, which is 20%. This makes understanding and communicating the percent easier and faster.