# Percent Error Problems

Videos and solutions to help Grade 7 students learn how to identify the original price as the whole and use their knowledge of percent and proportional relationships to solve multistep markup and markdown problems.

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Lessons for Grade 7
Common Core For Grade 7
## New York State Common Core Math Grade 7, Module 4, Lesson 8

### Lesson 8 Student Outcomes

• Given the exact value, x, of a quantity and an approximate value, a, of the quantity, students use the absolute
error, |a - x|, to compute the percent error by using the formula |a - x|/|x| x 100%.

• Students understand the meaning of percent error as the percent the absolute error is of the exact value.

• Students understand that when an exact value is not known, an estimate of the percent error can still be
computed when given a range determined by two inclusive values (e.g., if there are known to be between 6,000
and 7,000 black bears in New York, but the exact number is not known, the percent error can be
estimated to be (1000/6000)(100%) at most, which is 16 2/3 %).

Lesson 8 Classwork
Definitions:
__Absolute Error__: Given the exact value, x, of a quantity and an approximate value, a, of the quantity, the absolute error
is |a - x|

__Percent Error__: The percent error is the percent the absolute error is of the exact value, |a - x|/|x| x 100%, where x is the
exact value of the quantity and a is an approximate value of the quantity.

Example 1: How Far Off?

Three students measured the diagonal of a 15-inch screen (in inches) using a ruler.

Find the absolute error for the following problems. Explain what the absolute error means in context.

a. Taylor’s Measurement

b. Connor’s Measurement

c. Jordan’s Measurement

Example 2: How Right is Wrong?

a. Find the percent error for Taylor’s Measurement 1. What does this mean?

b. From Example 1, part (b), find the percent error for Connor’s Measurement 1. What does this mean?

c. From Example 1, part (c), find the percent error for Jordan’s Measurement 2. What does it mean?

d. What is the purpose of finding percent error?

Exercises 1–3

Calculate the percent error for Problems 1–3. Leave your final answer in fraction form, if necessary.

1. A realtor expected 18 people to show up for an open house, 25 but attended.

2. In science class, Mrs. Moore’s students were directed to weigh a 300 gram mass on the balance scale. Tina weighed
the object and reported 328 grams.

3. Darwin’s coach recorded that he had bowled 250 points out of 300 in a bowling tournament. However, the official
scoreboard showed that Darwin actually bowled points 225 out of 300.