Introduction to Decimals and Fractions

Hello, Year 5! Today, we’re going to learn how to write decimals as fractions. This is a fun skill that helps us understand how numbers work in different ways. Let’s get started!

What is a Decimal?

A decimal is a way of showing numbers that are not whole. For example, you might have the number 0.5. This means “five-tenths” of a whole.

What is a Fraction?

A fraction shows a part of a whole. It has two numbers: the top number (numerator) and the bottom number (denominator). For example, in the fraction \frac{1}{2}

, 1 is the numerator, and 2 is the denominator. This means we have one part of two equal parts.

How to Write Decimals as Fractions

Step 1: Look at the Decimal

First, identify the decimal you want to convert. For example, let’s take 0.75.

Step 2: Write it as a Fraction

To write this decimal as a fraction, place the decimal number over 1. So, 0.75 becomes:

\frac{0.75}{1}

Step 3: Remove the Decimal Point

Next, we need to get rid of the decimal point. Count how many places the decimal point moves to the right to become a whole number. In 0.75, it moves two places. This means we multiply both the top and bottom of our fraction by 100 (because there are two digits after the decimal):

\frac{0.75 \times 100}{1 \times 100} = \frac{75}{100}

Step 4: Simplify the Fraction

Now, let’s simplify the fraction. We can divide both the top and bottom by their greatest common divisor (GCD). For 75 and 100, the GCD is 25:

\frac{75 \div 25}{100 \div 25} = \frac{3}{4}

So, 0.75 is equal to the fraction \frac{3}{4}

.

Key Rules to Remember

  1. Identify the decimal number you want to convert.
  2. Write it over 1.
  3. Multiply by 10, 100, or 1000, depending on how many decimal places there are.
  4. Simplify the fraction if possible.

Tips and Tricks

  • Practice with different decimals to get better.
  • Use a calculator for tricky numbers to check your work.
  • Draw pictures or use objects to visualise fractions if you are a visual learner.

Questions to Practice

Easy Level Questions

  1. Write 0.2 as a fraction.
  2. Write 0.3 as a fraction.
  3. Write 0.4 as a fraction.
  4. Write 0.5 as a fraction.
  5. Write 0.6 as a fraction.
  6. Write 0.7 as a fraction.
  7. Write 0.8 as a fraction.
  8. Write 0.9 as a fraction.
  9. Write 0.25 as a fraction.
  10. Write 0.50 as a fraction.
  11. Write 0.1 as a fraction.
  12. Write 0.75 as a fraction.
  13. Write 0.05 as a fraction.
  14. Write 0.15 as a fraction.
  15. Write 0.85 as a fraction.
  16. Write 0.33 as a fraction.
  17. Write 0.9 as a fraction.
  18. Write 0.12 as a fraction.
  19. Write 0.4 as a fraction.
  20. Write 0.2 as a fraction.

Medium Level Questions

  1. Write 0.125 as a fraction.
  2. Write 0.375 as a fraction.
  3. Write 0.8 as a fraction.
  4. Write 0.67 as a fraction.
  5. Write 0.45 as a fraction.
  6. Write 0.92 as a fraction.
  7. Write 0.55 as a fraction.
  8. Write 0.04 as a fraction.
  9. Write 0.09 as a fraction.
  10. Write 0.18 as a fraction.
  11. Write 0.33 as a fraction.
  12. Write 0.99 as a fraction.
  13. Write 0.60 as a fraction.
  14. Write 0.85 as a fraction.
  15. Write 0.70 as a fraction.
  16. Write 0.22 as a fraction.
  17. Write 0.30 as a fraction.
  18. Write 0.01 as a fraction.
  19. Write 0.55 as a fraction.
  20. Write 0.66 as a fraction.

Hard Level Questions

  1. Write 0.625 as a fraction.
  2. Write 0.875 as a fraction.
  3. Write 0.3333 as a fraction.
  4. Write 0.142857 as a fraction.
  5. Write 0.6666 as a fraction.
  6. Write 0.01 as a fraction.
  7. Write 0.001 as a fraction.
  8. Write 0.125 as a fraction.
  9. Write 0.875 as a fraction.
  10. Write 0.5555 as a fraction.
  11. Write 0.789 as a fraction.
  12. Write 0.333 as a fraction.
  13. Write 0.888 as a fraction.
  14. Write 0.15 as a fraction.
  15. Write 0.95 as a fraction.
  16. Write 0.005 as a fraction.
  17. Write 0.0075 as a fraction.
  18. Write 0.007 as a fraction.
  19. Write 0.123 as a fraction.
  20. Write 0.999 as a fraction.

Answers and Explanations

Easy Level Answers

  1. \frac{1}{5}
  2. \frac{3}{10}
  3. \frac{2}{5}
  4. \frac{1}{2}
  5. \frac{3}{5}
  6. \frac{7}{10}
  7. \frac{4}{5}
  8. \frac{9}{10}
  9. \frac{1}{4}
  10. \frac{1}{2}
  11. \frac{1}{10}
  12. \frac{3}{4}
  13. \frac{1}{20}
  14. \frac{3}{20}
  15. \frac{17}{20}
  16. \frac{1}{3}
  17. \frac{9}{10}
  18. \frac{3}{25}
  19. \frac{2}{5}
  20. \frac{1}{5}

Medium Level Answers

  1. \frac{1}{8}
  2. \frac{3}{8}
  3. \frac{4}{5}
  4. \frac{67}{100}
  5. \frac{9}{20}
  6. \frac{23}{25}
  7. \frac{11}{20}
  8. \frac{1}{25}
  9. \frac{9}{100}
  10. \frac{9}{50}
  11. \frac{1}{3}
  12. \frac{99}{100}
  13. \frac{3}{5}
  14. \frac{17}{20}
  15. \frac{7}{10}
  16. \frac{11}{50}
  17. \frac{3}{10}
  18. \frac{1}{100}
  19. \frac{11}{20}
  20. \frac{33}{50}

Hard Level Answers

  1. \frac{5}{8}
  2. \frac{7}{8}
  3. \frac{1}{3}
  4. \frac{1}{7}
  5. \frac{2}{3}
  6. \frac{1}{100}
  7. \frac{1}{1000}
  8. \frac{1}{8}
  9. \frac{7}{8}
  10. \frac{5}{9}
  11. \frac{789}{1000}
  12. \frac{1}{3}
  13. \frac{8}{9}
  14. \frac{3}{20}
  15. \frac{19}{20}
  16. \frac{5}{1000}
  17. \frac{3}{400}
  18. \frac{7}{1000}
  19. \frac{123}{1000}
  20. \frac{999}{1000}

Now, practice these questions to become a pro at writing decimals as fractions! Happy learning!