LEMMA

Foundations

Decimals and percents

ALEKS · foundation repairTEAS math

Percent means per hundred, so converting moves the decimal point two places.

What this covers

part=percent×whole
  • Percent to decimal moves the point two places left. Fill empty places with zeros and write a zero before a lone point: 8.25% is 0.0825.
  • Decimal to percent: move the point two places right.
  • The word “of” means multiply.
  • To order mixed forms, rewrite every value as hundredths: 45%, 21/50 and 0.43 become 45, 42 and 43 out of 100.
  • Percent change divides the change by the original value, never by the new one.

Worked example

Worked example

What is 18% of 250?

  1. 0.18⋅25018% becomes the decimal 0.18.
  2. 45Multiply, because “of” means times.
Another worked example

Convert 12.5% to a decimal and fraction, then find 12.5% of 80.

  1. 12.5%=10012.5​=0.125=81​The percent sign divides by 100, including when the percent is noninteger.
  2. 80⋅81​=10Use 80 as the baseline and multiply by the rate.

A common mistake

A mistake Lemma catches

From 0.75P=60

P=60⋅1.25P=0.7560​

“The 25% came off the original price, not off $60, so adding 25% of 60 back uses the wrong base: 60 + 0.25 · 60 = 75. The sale price is 75% of the original, 0.75P = 60, so divide both sides by 0.75: 60 ÷ 0.75 = 80. Check: 25% of 80 is 20, and 80 − 20 = 60.”

Try one

Sample problem

Find 25% of 80.

25% of 80

Practice percents free

No account, no email. Every line you type is checked by the same computer algebra system as the worked example above.

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