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Math : Conversion of Percentages to Decimals and Fractions – Lesson 3

This lesson is part of the Lesson on Conversion Series. The conversion of Percentages to Decimals or Fractions is usually part of the set of questions on numerical ability. You may also need this skill when solving word problems on ratio and proportion, and on word problems involving discounts, interest, and profit.

Before we begin our lesson, let me again remind you some basic points to remember when converting Fractions, Decimals, and Percent:

  • In a fraction, the top number is the Numerator and the bottom number is the Denominator.
  • Be careful when counting the decimal places. Here, decimal place refers to the number of digits to the right of a decimal point. So, in 0.25, 25 has two decimal places; in 0.001, 1 has three decimal places; in 0.058, 58 has three decimal places; and in 0.06, 6 has two decimal places.
  • The number to the left of the decimal point is the integer. The number to the right of the decimal point is the fractional part.
  • ‘Percent’ is a number or ratio expressed as a fraction of 100.

Converting a Percent to a Decimal:

  1. Simply move the decimal point two places to the left.
  2. Remove the percent sign.

Examples:

  1. 25% = 0.25
  2. 9% = 0.09

Converting a Percent to a Fraction:

  1. Remove the percent sign.
  2. Find the numerator: The number is the numerator
  3. Find the denominator: The denominator is always 100 unless the number has a fractional part.
  4. If the number has a fractional part (refers to numbers to the right of the decimal point), count the decimal places and then remove the decimal point.
    The number of decimal places indicates the number of zeroes you need to add to the denominator – 100.

Examples:

  1. 25% = ?
    Find the numerator: 25
    Find the denominator: 100 (because 25% has no fractional part)
    Thus 25% = 25/100
  2. 0.8% = ?
    Find the numerator: 8
    Find the denominator: 0.8 is a fractional part, and there is 1 decimal place. So you add 1 zero to 100, making it 1000.
    Thus 0.8% = 8/1000

The Lesson Series on Conversion


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