Converting between FDP | Mathematics for GCSE/IGCSE - Year 11 PDF Download

FDP Conversions

To convert a percentage to a decimal, divide by 100, which involves moving the digits two places to the right.

• For instance, 6% as a decimal would be 6 ÷ 100 = 0.06
• Similarly, 40% as a decimal would be 40 ÷ 100 = 0.4
• Another example is 350% as a decimal, which would be 350 ÷ 100 = 3.5
• Lastly, 0.2% as a decimal would be 0.2 ÷ 100 = 0.002

How do I convert from a decimal to a percentage?

To convert a decimal to a percentage, multiply by 100, shifting the digits two places to the left and adding a % sign.

• For example, 0.35 as a percentage would be 0.35 × 100 = 35%
• Likewise, 1.32 as a percentage would be 1.32 × 100 = 132%
• Additionally, 0.004 as a percentage would be 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 3/10
  • 1.1 is 11/10
• If it has two decimal places, write the digits over 100
  • 0.07 is 7/100
  • 0.13 is 13/100
  • 30.01 is 3001/100
• If it has n decimal places, write the digits over 10^n
  • 0.513 is 513/1000
  • 0.0007 is 7/10000
• Learn simple recurring decimals as fractions
  • 0.33333... = 1/3
  • 0.66666... = 2/3
• Whole numbers can be written as fractions (by writing them over 1)
  • 5 is 5/1

How do I convert from a percentage to a fraction?

Write the percentage over 100

• 37% is 37/100

How do I convert from a fraction to a decimal?

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

How do I convert from a fraction to a percentage?

Change fractions into decimals (see above), then multiply by 100

• 4/5 = 8/10 which is 0.8 as a decimal, which is 0.8 × 100 = 80%.

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/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)
  

How do I write recurring decimals as fractions?

When dealing with recurring decimals, we can convert them into fractions following a systematic approach:

• Write out the recurring decimal as f and identify the repeating pattern.
• Multiply both sides of the equation by 10 successively until the recurring part aligns.
• Subtract the two lines to eliminate the recurring part.
• Divide both sides to express f as a fraction in its simplest form.