Fractions and Decimal Equivalents
Fractions and Decimal Equivalents is the Year 4 topic covering converting confidently between fractions and decimals, including key equivalents such as 1/2 = 0.5 and 1/4 = 0.25, and comparing and ordering decimals with up to two decimal places.
Before you start
Make sure you're comfortable with these topics first:
Method
- Remember that the denominator of a fraction tells you how many equal parts make one whole: tenths (denominator 10) have one decimal place, and hundredths (denominator 100) have two decimal places.
- To write a fraction with denominator 10 as a decimal, put the numerator straight after the decimal point, e.g. 7/10 = 0.7.
- To write a fraction with denominator 100 as a decimal, write the numerator as a two-digit number after the decimal point, filling an empty tens column with a zero, e.g. 6/100 = 0.06.
- Learn three key equivalents by heart, since they come up in measures and money as well as pure fraction questions: 1/2 = 0.5, 1/4 = 0.25 and 3/4 = 0.75.
- To find an equivalent fraction, multiply the numerator and denominator by the same number, e.g. multiplying 1/2 by 5/5 gives 5/10, which converts straight to 0.5.
- To compare two decimals with a different number of decimal places, first write them with the same number of decimal places by adding trailing zeros, e.g. compare 0.6 and 0.45 as 0.60 and 0.45.
- Use a place-value grid (ones, tenths, hundredths) or a 100-square diagram to check that a fraction-to-decimal conversion makes sense.
Worked example
Write 3/4 and 9/10 as decimals, then state which is greater.
- Convert 3/4 to an equivalent fraction with denominator 100: multiply the numerator and denominator by 25, giving 75/100.
- Write 75/100 as a decimal: 0.75.
- Convert 9/10 to a decimal directly, since it already has denominator 10: 9/10 = 0.9.
- Compare 0.75 and 0.90 (writing 0.9 as 0.90 so both have two decimal places): 90 hundredths is greater than 75 hundredths.
- So 9/10 (0.9) is greater than 3/4 (0.75).
Practice questions
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Q1Write 4/10 as a decimal.Show answer
Answer: 0.4
Q2Write 37/100 as a decimal.Show answer
Answer: 0.37
Q3Write 0.8 as a fraction with a denominator of 10.Show answer
Answer: 8/10 (which simplifies to 4/5)
Q4A stick of seaside rock is 0.65 m long. Write 0.65 as a fraction of a metre, using hundredths.Show answer
Answer: 65/100 m
Q5Which is bigger, 3/10 or 27/100? Explain how you know.Show answer
Answer: 3/10 is bigger, because 3/10 is equivalent to 30/100, and 30/100 is greater than 27/100.
Q6Find the missing numerator: 3/4 = ?/100.Show answer
Answer: 75, because 3/4 = 75/100 (multiply the numerator and denominator by 25).
Q7Nadia has read 0.9 of her reading book. Write 0.9 as a fraction in tenths, then in hundredths.Show answer
Answer: 9/10, which is equivalent to 90/100.
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
Three friends each complete part of a 100-piece jigsaw puzzle: Aisha completes 0.55 of the puzzle, Ben completes 7/10 of the puzzle, and Freya completes 3/4 of the puzzle. Write the three amounts in order, starting with the smallest.
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Write 17/20 as a decimal. Show your method, including any equivalent fraction you use.
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Circle the decimal that is equivalent to 4/5: 0.4 0.45 0.8 0.54
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Free printable worksheet
Want more practice on paper? Download the fractions and decimal equivalents worksheet pack - 5 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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