Converting between FDP (CIE IGCSE Maths: Extended)

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 
• 1.1 is 
• If it has two decimal places, write the digits over 100
• 0.07 is 
• 0.13 is  
• 30.01 is  
• If it has n decimal places, write the digits over 10ⁿ
• 0.513 is 
• 0.0007 is  
• Learn simple recurring decimals as fractions
• 0.33333… =   is   and 0.66666… =  is 
• Whole numbers can be written as fractions (by writing them over 1)
• 5 is 

 

How do I convert from a percentage to a fraction?

• Write the percentage over 100
• 37% is

 

How do I convert from a fraction to a decimal?

• Fractions written over powers of 10 are quicker
•  which is 0.6
•  which is 0.35
•  which is 0.002

 

How do I convert from a fraction to a percentage?

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

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 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)
  • 
  • 
  • 

 

Converting recurring decimals to 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)