Testinar Grade 7 math

Percent Error: How Close Are Your Estimates?

Students will build Grade 7 mastery of percent error: how close are your estimates? using models, equations, and test-style reasoning.

CH02-07 Percents and Financial Literacy

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

Jonah estimated the length of a pencil to be \(7\) inches, but the actual length is \(8\) inches. What is the percent error?
1. \(10.0\%\)
2. \(87.5\%\)
3. \(14.3\%\)
4. \(12.5\%\)
Maria guessed that a book weighs \(2\) pounds, but it actually weighs \(2.5\) pounds. What is the percent error?
1. \(80\%\)
2. \(25\%\)
3. \(50\%\)
4. \(20\%\)
A student estimated a room to be \(12\) meters wide, but the actual width is \(10\) meters. What is the percent error?
1. \(2\%\)
2. \(15\%\)
3. \(10\%\)
4. \(20\%\)
Leo predicted that he would run a race in \(45\) seconds, but he actually completed it in \(50\) seconds. What is the percent error in his prediction?
1. \(90\%\)
2. \(11.1\%\)
3. \(5\%\)
4. \(10\%\)
A baker estimated \(120\) cups of flour were needed, but the recipe actually required \(100\) cups. What is the percent error?
1. \(83.3\%\)
2. \(16.7\%\)
3. \(22.2\%\)
4. \(20\%\)
An estimate of \(42\) meters has a percent error of \(16.7\%\) compared to the actual distance. What was the actual distance?
1. \(35\) meters
2. \(48\) meters
3. \(36\) meters
4. \(50\) meters
What is the percent error for the height estimate?
1. \(91.7\%\)
2. \(9.1\%\)
3. \(8.3\%\)
4. \(6\%\)
A student estimated the population of a city to be \(500,000\), but the actual population is \(450,000\). What is the percent error?
1. \(88.9\%\)
2. \(10\%\)
3. \(15\%\)
4. \(11.1\%\)

Teacher and parent reference

Answer key and explanations

D. \(12.5\%\)
Percent error \(=\frac{|\text{estimate}-\text{actual}|}{|\text{actual}|}\times100\%=\frac{|7-8|}{8}\times100\%=12.5\%\).
D. \(20\%\)
Percent error \(=\frac{|2-2.5|}{2.5}\times100\%=\frac{0.5}{2.5}\times100\%=20\%\).
D. \(20\%\)
Percent error \(=\frac{|12-10|}{10}\times100\%=\frac{2}{10}\times100\%=20\%\).
D. \(10\%\)
Percent error \(=\frac{|45-50|}{50}\times100\%=\frac{5}{50}\times100\%=10\%\).
D. \(20\%\)
Percent error \(=\frac{|120-100|}{100}\times100\%=\frac{20}{100}\times100\%=20\%\).
D. \(50\) meters
If percent error is \(16.7\%\), then \(\frac{|42-\text{actual}|}{|\text{actual}|}\times100\%=16.7\%\). Testing \(50\): \(\frac{|42-50|}{50}\times100\%=16\%\approx 16.7\%\).
C. \(8.3\%\)
Percent error \(=\frac{|66-72|}{72}\times100\%=\frac{6}{72}\times100\%=8.3\%\).
D. \(11.1\%\)
Percent error \(=\frac{|500000-450000|}{450000}\times100\%=\frac{50000}{450000}\times100\%\approx 11.1\%\).