# Greatest Possible Error, Percent Error and Percent of Change

Videos, worksheets, stories and songs to help Grade 9 students learn about percent of change, Greatest Possible Error of a measurement and percent error.

Related Topics: More Math Lessons for Grade 9

Greatest possible error and rounding measurements
What is Greatest Possible Error (GPE)?
The greatest possible error of a measurement is how far off a measurement can be and still round to what is written. It is half the precision.

This video explains why the Greatest Possible Error (GPE) is one half of the precision. How to calculate the Greatest Possible Error from word problems? Examples:
1. You measure your brother and record his height as 49in. What is your greatest possible error?

2. You weigh a bunch of bananas at the grocery store. The scale reads 18.7oz. What is your greatest possible error? How to calculate the Greatest Possible Error using a shortcut and how to calculate the percent error?
Examples:
Find the Greatest Possible Error (GPE) of the following?
a. 54.67 ft.
b. 34.1 cm
c. 35.678 in

Do you notice a pattern? If so what is it?

Using the pattern complete the following GPE.
a. 15.25 ft
b. 34.467 cm
c. 13.4 cm
d. 81.324 mm

Find the Percent Error
a. 4.007 oz
b. 15.6 in
c. 23 cm
d. 6.57 lbs
e. 13.4 ft
f. 13.445 cm

How to calculate the percent error of a measurement?
The percent error is the Greatest Possible Error (GPE) divided by the measurement multiply by 100%.
(Errata: In the first example, the given precision is 1m and so the GPE should be 0.5m).

How to find Percent of Change and Greatest Possible Error?
Example 1: Find the percent of change to the nearest percent. A CD goes down in price from \$15.99 to \$9.99

Example 2: Find the percent of change to the nearest percent. A CD goes up in price from \$9.99 to \$15.99

Example 3: The weight scales shows a weight of 145.2 pounds. What is the greatest possible error?

Example 4: A measurement is 6 feet? What is the greatest possible error? How to calculate percent of change and greatest possible error?
Percent of change is the amount of change divided by the original amount.
Example 1: The price of a shirt decreased from \$32.95 to \$28.95. Find the percent of decrease.

Example 2: Between 1940 and 1980, the federal budget increased from \$9.5 billion to \$725.3 billion. What was the percent of increase in the budget?

The Greatest Possible Error is one half of the measuring unit.
Example 3: You read the bathroom scale as 122 lb. What is your greatest possible error? What is your % error?

Example 4: When the garden plot was measured, the dimensions were 156 in by 84 in. Use the greatest possible error to find the minimum and maximum possible areas. What is your % error?

Example 5: Suppose you measure a library book and record its width as 17.6 cm. Find the percent of error in your measurement.

Example 6: A small jewelry box measures 7.4cm by 12.2cm by 4.2cm. Find the percent error in calculating the volume.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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