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350 Converting a Percent to a Decimal or a Fraction

How to convert the "devil remover notation of %" and create a usable number

a fraction capable calculator may be helpful

We know from lesson 340 A history of Percents, the word "percent" originally meant "cents", and was used back in the dark ages by merchant to remove evil spirits form numbers.

percent signs were used to cast out the demons from numbers

Unfortunately, since a % sign is nothing more than an 'evil spirit remover', we must convert any % numbers into either decimals or fractions before we can use them.


the winds of percent changes

Since the word "percent" originally meant "cents", changing a percent to a decimal is easy; just write it as money in dollar notation, and then remove the dollar sign.

Let's look at a few:

  1. 35% or 35 cents = $.35 or 0.35 (Some people put the zero in front of the decimal to draw attention to the decimal.)
  2. 8% or 8 cents = $.08 or 0.08
  3. 150% or 150 cents = $1.50 or 1.50=1.5
    (Remember the zero in the hundredths spot of the decimal can be dropped without changing the value.)

*NOTICE that in every case the decimal notation places the decimal point 2 spots to the LEFT of the % notation.

This actually ALWAYS HAPPENS. To change a % to a decimal, simply drop the percent sign and move the decimal two spots left.

NOTE: If you don't see any decimal point on a percent number, like in the examples above, remember that it is always to the right of the one's place. For example, 35%=35.%.

Let's look at a few harder ones:

  1. 3.5% or 3.5 cents = $.035 or 0.035
  2. .5% or .5 cents or half a cent =$.005 or 0.005
  3. 4,521% or 4521 cents = $45.21 0r 45.21
  4. 68 3/5% or 68.6 cents* = $.686 or 0.686
    *Notice that above 3/5 =.6, so we just changed the original % to a decimal before getting dollar


percents to fractions a logical relationship

Now that you can write percents as decimals, to get the fraction you simply say the decimal formally.

For example:

  1. 35% = 0.35 which is read, "thirty-five hundredths", so we write the fraction 35/100. Now this will reduce to 7/20, so 35% = 7/20.
  2. 752% =7.52 which is read, "seven and fifty-two hundredths", so we write the mixed number 7 52/100. This will reduce to 7 13/25.
  3. .24% = 0.0024 which is read,
    "twenty-four ten-thousandths", so we write the fraction
    24/10,000. This fraction reduces to 3/1,250.

  1. What is 45% as a decimal and as a fraction? (answer)
  2. Give the fraction and decimal for 250%. (answer)
  3. Write 3 1/2% as a decimal and a fraction. (answer)

Click here to get some teaching tips for this lesson.

340 The History of Percent

360 set up a proportion to solve % problems

370 set up an equation to solve percent problems

The Customizable Percent Test

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