Converting between FDP (Edexcel GCSE Maths)

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FDP Conversions

How do I convert from a percentage to a decimal?

  • Divide by 100 (move digits two places to the right)
    • 6% as a decimal is 6 ÷ 100 = 0.06
    • 40% as a decimal is 40 ÷ 100 = 0.4
    • 350% as a decimal is 350 ÷ 100 = 3.5
    • 0.2% as a decimal is 0.2 ÷ 100 = 0.002

 

How do I convert from a decimal to a percentage?

  • Multiply by 100 (move digits two places to the left and add a % sign)
    • 0.35 as a percentage is  0.35 × 100 = 35%
    • 1.32 as a percentage is 1.32 × 100 = 132%
    • 0.004 as a percentage is 0.004 × 100 = 0.4%

 

How do I convert from a decimal to a fraction?

  • If it has one decimal place, write the digits over 10
    • 0.3 is 3 over 10
    • 1.1 is 11 over 10
  • If it has two decimal places, write the digits over 100
    • 0.07 is 7 over 100
    • 0.13 is  13 over 100
    • 30.01 is  3001 over 100
  • If it has n decimal places, write the digits over 10n
    • 0.513 is 513 over 1000
    • 0.0007 is  fraction numerator 7 over denominator 10 space 000 end fraction
  • Learn simple recurring decimals as fractions
    • 0.33333… = 0.3 with dot on top  is  1 third and 0.66666… =  0.6 with dot on top is 2 over 3
  • Whole numbers can be written as fractions (by writing them over 1)
    • 5 is 5 over 1

 

How do I convert from a percentage to a fraction?

  • Write the percentage over 100
    • 37% is 37 over 100

 

How do I convert from a fraction to a decimal?

Order by Size Notes fig2a

  • Fractions written over powers of 10 are quicker
    • 3 over 5 equals 6 over 10 which is 0.6
    • 7 over 20 equals 35 over 100 which is 0.35
    • 1 over 500 equals 2 over 1000 which is 0.002

 

How do I convert from a fraction to a percentage?

  • Change fractions into decimals (see above), then multiply by 100
    • 4 over 5 equals 8 over 10 which is 0.8 as a decimal, which is 0.8 × 100 = 80%

Examiner Tip

  • A calculator can be used to check conversions between fractions and decimals (even if the question says to show working without a calculator)

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Recurring Decimals

What are recurring decimals?

  • A rational number is any number that can be written as an integer (whole number) divided by another integer
    • A number written as p over q in its simplest form, where p and q are integers is rational
  • When you write a rational number as a decimal, you either get a decimal that stops (e.g. ¼ = 0.25), called a "terminating" decimal, or one that repeats with a pattern (e.g. ⅓ = 0.333333…), called a "recurring" decimal
  • The recurring part can be written with a dot (or dots on the first and last recurring digit)
    • 0.3333... space equals space 0.3 with dot on top
    • 0.121212... space equals 0.1 with dot on top 2 with dot on top
    • 0.325632563256... equals 0.3 with dot on top 25 6 with dot on top

 

How do I write recurring decimals as fractions?

Write out the first few decimal places to show the recurring pattern and then:

  1. Write the recurring decimal f = … (some similar methods use x = ...)
  2. Multiply both sides by 10 repeatedly until two lines have the same recurring decimal part (in order)
  3. Subtract those two lines
  4. DIVIDE both sides to get f = … (and cancel if necessary to get fraction in lowest terms)

Worked example

Write 0.3 with dot on top 7 with dot on top as a fraction in its lowest terms,

0.3 with dot on top 7 with dot on top means 0.3737373737...

Use a variable to represent this number.

x equals 0.3737373737...

Multiply both sides by 100 to get another number with the same recurring decimal part.

100 x equals 37.3737373737...

Subtract the two equations to cancel out the recurring decimal parts.

Divide both sides by 99

x equals 37 over 99

Type the fraction in your calculator and change to a decimal to check it is correct.

bold 37 over bold 99

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Amber

Author: Amber

Expertise: Maths

Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.