Percent as Ratio Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
A student scores 3434 out of 4040 on a test. Express this as a percentage. Then determine what score out of 4040 corresponds to 90%90\%.

Solution

  1. 1
    Score as a ratio: 3440\dfrac{34}{40}. Convert to percent: 3440×100=85%\dfrac{34}{40} \times 100 = 85\%.
  2. 2
    For 90%90\%: set up s40=90100\dfrac{s}{40} = \dfrac{90}{100}. Solve: s=40×0.90=36s = 40 \times 0.90 = 36.
  3. 3
    A score of 3636 out of 4040 corresponds to 90%90\%.

Answer

34/40=85%34/40 = 85\%; a score of 36/4036/40 equals 90%90\%.
Percent is a standardised ratio with denominator 100100, allowing easy comparison of scores on different scales. Going the other direction — finding the raw score for a given percent — requires multiplying the total by the percent expressed as a decimal.

About Percent as Ratio

A ratio comparing a quantity to 100, written with the % symbol; 'per cent' literally means 'per hundred'.

Learn more about Percent as Ratio →

More Percent as Ratio Examples

Example 1 easy

A shirt originally costs [formula]45[formula]20%$ off. Find the sale price.

Example 3 easy

Convert each to the indicated form: (a) [formula] to percent, (b) [formula] to decimal, (c) [formula

Example 4 medium

A population grew from [formula] to [formula]. What is the percent increase?

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