Decimals and Fractions
Decimals and fractions are two ways to show the same value. To convert a decimal to a fraction, count the decimal places to set the denominator 10, 100 or 1000, then simplify if you can. So 0.01 = 1/100.
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The Decimal Place Value
- The decimal point separates the whole number and the fractional part.
- Each place to the right of the decimal point is 10 times smaller: tenths, hundredths, thousandths.
Converting Decimals (Less Than 1) to Fractions
- Write the decimal as a fraction over 10, 100, or 1000.
- Simplify the fraction if possible. For example, .
Converting Decimals (Greater Than 1) to Fractions
- Split the number into a whole number and a decimal part.
- Convert the decimal part to a fraction, then combine with the whole number.
- For example,
Practice Questions
Test your understanding
What is 0.01 as a fraction in its simplest form?
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In 0.01 the digit 1 sits in the hundredths column, so 0.01 means 1 hundredth.
As a fraction that is , which is already in its simplest form.
What is 0.4 as a fraction in its simplest form?
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0.4 has one decimal place, so it means 4 tenths: .
Dividing the numerator and the denominator by 2 gives , which is the simplest form.
Convert 0.45 to a fraction in its simplest form.
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0.45 means 45 hundredths, so .
The highest common factor of 45 and 100 is 5, so divide both the numerator and the denominator by 5: and .
So . Checking: .
Which fraction is equal to 0.28 in its simplest form?
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0.28 means 28 hundredths, so .
The highest common factor of 28 and 100 is 4, so divide both parts by 4: and .
So . Checking: .
Convert 0.22 to a fraction in its simplest form.
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0.22 means 22 hundredths, so .
The highest common factor of 22 and 100 is 2, so divide both parts by 2: and .
So . Checking: .
Convert 0.375 to a fraction in its simplest form.
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0.375 means 375 thousandths, so .
The highest common factor of 375 and 1000 is 125, so divide both parts by 125: and .
So . Checking: .
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Interactive Activity
Practice converting decimals to fractions
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Frequently asked questions
The questions students bump into most on this topic
Both show parts of a whole; they are two ways of writing the same value. A decimal uses a decimal point with tenths, hundredths and thousandths places, so 0.1 is one tenth, 0.01 one hundredth and 0.001 one thousandth. A fraction writes the same part as a numerator over a denominator: 0.1 = 1/10 and 0.01 = 1/100.
Count the digits after the decimal point: one place means the denominator is 10, two means 100, three means 1,000. Write the digits without the point on top, then simplify. So 0.4 = 4/10 = 2/5, and 0.028 = 28/1,000 = 7/250. The box question 0.35 works the same way: 35/100 = 7/20.
0.75 is three quarters. It has two decimal places, so write 75 over 100, then divide the top and bottom by 25 to get 3/4. Three quarters means three out of four equal parts, which is why 0.75 of £1 is 75p.
Split the number into its whole part and its decimal part, convert only the decimal part, then put them back together. 1.75 is 1 + 0.75, and 0.75 is 3/4, so 1.75 = 1 3/4, a mixed number. Converting the whole thing as 175/100 also works, but simplifying it is harder.
Use money. £1 is the whole; 10p is one tenth of it, which can be written as 1/10 or as 0.1; 1p is one hundredth, 1/100 or 0.01. Then look at prices: £0.75 is 75p, which is three quarters of a pound, so 0.75 and 3/4 are the same amount.
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