Year 7 Maths: Convert Fractions to Terminating Decimals

What is a Terminating Decimal?

A terminating decimal is a number that has a finite number of digits after the decimal point. For example, 0.5 and 0.75 are terminating decimals because they stop after one and two digits, respectively.

How to Convert Fractions to Terminating Decimals

To convert a fraction to a terminating decimal, follow these steps:

Step 1: Simplify the Fraction

If the fraction can be simplified, do that first! For example, the fraction $$\frac{4}{8}$$ can be simplified to $$\frac{1}{2}$$ .

Step 2: Check the Denominator

Next, check the denominator (the bottom number of the fraction). A fraction will convert to a terminating decimal if the denominator can be written as a product of the numbers 2 and/or 5 only.

• For example, the fraction $$\frac{1}{4}$$ has a denominator of 4, which is $$2^2$$ , so it will convert to a terminating decimal.
• But, the fraction $$\frac{1}{3}$$ has a denominator of 3, which is neither 2 nor 5, so it will not convert to a terminating decimal.

Step 3: Perform the Division

If your fraction has a suitable denominator, divide the numerator (the top number) by the denominator.

• For example, to convert $$\frac{1}{4}$$ to a decimal, you divide 1 by 4, which equals 0.25.

Key Rules for Terminating Decimals

1. Denominator Check: Only fractions with denominators made of the prime factors 2 and 5 will convert to terminating decimals.
2. Perform Division: Use long division or a calculator to find the decimal.
3. Practice: The more you practice, the easier it becomes!

Tips and Tricks

• Remember that fractions like $$\frac{2}{5}, \frac{3}{10},$$ and $$\frac{7}{25}$$ will convert easily because their denominators are made from 2s and 5s.
• If you encounter a fraction with a denominator like 12, try to simplify it first. For example, $$\frac{1}{12}$$ does not convert to a terminating decimal because 12 has a factor of 3.

Practice Questions

Easy Level Questions

1. Convert $$\frac{1}{2}$$ to a decimal.
2. Convert $$\frac{3}{4}$$ to a decimal.
3. Convert $$\frac{1}{5}$$ to a decimal.
4. Convert $$\frac{2}{10}$$ to a decimal.
5. Convert $$\frac{3}{8}$$ to a decimal.
6. Convert $$\frac{1}{20}$$ to a decimal.
7. Convert $$\frac{5}{10}$$ to a decimal.
8. Convert $$\frac{2}{5}$$ to a decimal.
9. Convert $$\frac{1}{100}$$ to a decimal.
10. Convert $$\frac{3}{2}$$ to a decimal.

Medium Level Questions

11. Convert $$\frac{7}{4}$$ to a decimal.
12. Convert $$\frac{9}{20}$$ to a decimal.
13. Convert $$\frac{5}{8}$$ to a decimal.
14. Convert $$\frac{6}{25}$$ to a decimal.
15. Convert $$\frac{1}{8}$$ to a decimal.
16. Convert $$\frac{15}{100}$$ to a decimal.
17. Convert $$\frac{3}{5}$$ to a decimal.
18. Convert $$\frac{4}{5}$$ to a decimal.
19. Convert $$\frac{1}{16}$$ to a decimal.
20. Convert $$\frac{11}{20}$$ to a decimal.

Hard Level Questions

21. Convert $$\frac{13}{50}$$ to a decimal.
22. Convert $$\frac{7}{8}$$ to a decimal.
23. Convert $$\frac{3}{16}$$ to a decimal.
24. Convert $$\frac{17}{40}$$ to a decimal.
25. Convert $$\frac{19}{80}$$ to a decimal.
26. Convert $$\frac{21}{100}$$ to a decimal.
27. Convert $$\frac{1}{12}$$ to a decimal.
28. Convert $$\frac{11}{25}$$ to a decimal.
29. Convert $$\frac{9}{50}$$ to a decimal.
30. Convert $$\frac{23}{100}$$ to a decimal.

Answers and Explanations

Easy Level Answers

1. $$\frac{1}{2} = 0.5$$ . This is because when you divide 1 by 2, you get 0.5.
2. $$\frac{3}{4} = 0.75$$ . Dividing 3 by 4 gives you 0.75, which is a terminating decimal.
3. $$\frac{1}{5} = 0.2$$ . When you divide 1 by 5, you get 0.2.
4. $$\frac{2}{10} = 0.2$$ . This simplifies to $$\frac{1}{5}$$ , which we already know is 0.2.
5. $$\frac{3}{8} = 0.375$$ . Dividing 3 by 8 results in 0.375.
6. $$\frac{1}{20} = 0.05$$ . When you divide 1 by 20, you get 0.05.
7. $$\frac{5}{10} = 0.5$$ . This is the same as $$\frac{1}{2}$$ , which is 0.5.
8. $$\frac{2}{5} = 0.4$$ . Dividing 2 by 5 gives you 0.4.
9. $$\frac{1}{100} = 0.01$$ . When you divide 1 by 100, the result is 0.01.
10. $$\frac{3}{2} = 1.5$$ . Dividing 3 by 2 results in 1.5.

Medium Level Answers

11. $$\frac{7}{4} = 1.75$$ . Dividing 7 by 4 gives you 1.75, which is a terminating decimal.
12. $$\frac{9}{20} = 0.45$$ . When you divide 9 by 20, you get 0.45.
13. $$\frac{5}{8} = 0.625$$ . Dividing 5 by 8 results in 0.625.
14. $$\frac{6}{25} = 0.24$$ . When you divide 6 by 25, the result is 0.24.
15. $$\frac{1}{8} = 0.125$$ . Dividing 1 by 8 gives you 0.125.
16. $$\frac{15}{100} = 0.15$$ . When you divide 15 by 100, you get 0.15.
17. $$\frac{3}{5} = 0.6$$ . Dividing 3 by 5 results in 0.6.
18. $$\frac{4}{5} = 0.8$$ . When you divide 4 by 5, the result is 0.8.
19. $$\frac{1}{16} = 0.0625$$ . Dividing 1 by 16 gives you 0.0625.
20. $$\frac{11}{20} = 0.55$$ . When you divide 11 by 20, the result is 0.55.

Hard Level Answers

21. $$\frac{13}{50} = 0.26$$ . Dividing 13 by 50 gives you 0.26.
22. $$\frac{7}{8} = 0.875$$ . When you divide 7 by 8, you get 0.875.
23. $$\frac{3}{16} = 0.1875$$ . Dividing 3 by 16 results in 0.1875.
24. $$\frac{17}{40} = 0.425$$ . When you divide 17 by 40, the result is 0.425.
25. $$\frac{19}{80} = 0.2375$$ . Dividing 19 by 80 gives you 0.2375.
26. $$\frac{21}{100} = 0.21$$ . When you divide 21 by 100, you get 0.21.
27. $$\frac{1}{12} = 0.0833…$$ . This does not terminate, as 12 has a factor of 3.
28. $$\frac{11}{25} = 0.44$$ . Dividing 11 by 25 results in 0.44.
29. $$\frac{9}{50} = 0.18$$ . When you divide 9 by 50, you get 0.18.
30. $$\frac{23}{100} = 0.23$$ . Dividing 23 by 100 gives you 0.23.

Feel free to ask any questions if you need further explanations! Happy learning!