14.1: Number Talk: Estimating a Percentage of a Number
Estimate.
25% of 15.8
9% of 38
1.2% of 127
0.53% of 6
0.06% of 202
Let’s use percentages to describe other situations that involve error.
Estimate.
25% of 15.8
9% of 38
1.2% of 127
0.53% of 6
0.06% of 202
A micrometer is an instrument that can measure lengths to the nearest micron (a micron is a millionth of a meter). Would this instrument be useful for measuring any of the following things? If so, what would the largest percent error be?
The thickness of an eyelash, which is typically about 0.1 millimeters.
The diameter of a red blood cell, which is typically about 8 microns.
The diameter of a hydrogen atom, which is about 100 picometers (a picometer is a trillionth of a meter).
A metal measuring tape expands when the temperature goes above $50^\circ\text{F}$. For every degree Fahrenheit above 50, its length increases by 0.00064%.
The temperature is 100 degrees Fahrenheit. How much longer is a 30-foot measuring tape than its correct length?
What is the percent error?
Percent error can be used to describe any situation where there is a correct value and an incorrect value, and we want to describe the relative difference between them. For example, if a milk carton is supposed to contain 16 fluid ounces and it only contains 15 fluid ounces:
We can also use percent error when talking about estimates. For example, a teacher estimates there are about 600 students at their school. If there are actually 625 students, then the percent error for this estimate was 4%, because $625 - 600 = 25$ and $25 \div 625 = 0.04$.
The difference between the correct value and the incorrect value, expressed as a percentage of the correct value.