Converting fractions to terminating decimals | Maths | Quizalize & Oak National Academy

Starter quiz

Fractions where the numerator is less than the denominator are called ______ fractions.
- 'proper' ✓
The integer that is equivalent to the fraction $30 \over 5$ is ______.
- '6' ✓
Write $3\frac{2}{7}$ as an improper fraction.
- $\frac{23}{2}$
- $\frac{21}{7}$
- $\frac{22}{7}$
- $\frac{23}{7}$ ✓
- $\frac{24}{7}$
Write the correct symbol (<, > or =) to make the statement true: $17 \frac {1}{2}$ ______ $\frac {69}{4}$
- '>' ✓
Starting with the smallest, put these fractions and mixed numbers in order of size.
- 1
  
  ⇔
  
  $1\frac {1}{8}$
- 2
  
  ⇔
  
  $1\frac {1}{4}$
- 3
  
  ⇔
  
  $\frac {13}{8}$
- 4
  
  ⇔
  
  $1\frac {3}{4}$
- 5
  
  ⇔
  
  $2\frac {1}{8}$
- 6
  
  ⇔
  
  $\frac {18}{8}$
A gardener puts up a fence around a rectangular garden. Each fence panel is 1 metre long and costs £25. What is the total cost of the fencing? £______
- '650' ✓

Decimals that have a finite number of digits after the decimal point are called ______ decimals.
- 'terminating' ✓
Without using a calculator, work out the decimal value of $\frac {7}{8}$ . ______
- '0.875' ✓
Select all the fractions that can be written as terminating decimals.
- $\frac {7}{16}$ ✓
- $\frac {7}{5}$ ✓
- $\frac {7}{15}$
- $\frac {7}{20}$ ✓
- $\frac {7}{30}$
Sofia uses her calculator to convert $0.3756$ to a fraction. She gets an answer of $\frac {939}{\square}$ . What number should go in the square? ______
- '2500' ✓
Match each fraction to its terminating decimal. You can use a calculator for this question.
- $\frac {82}{125}$
  
  ⇔
  
  $0.656$ ✓
- $\frac {3281}{5000}$
  
  ⇔
  
  $0.6562$ ✓
- $\frac {21}{32}$
  
  ⇔
  
  $0.65625$ ✓
- $\frac {26}{40}$
  
  ⇔
  
  $0.65$ ✓
- $\frac {180}{300}$
  
  ⇔
  
  $0.6$ ✓
Lucas says that $66 \over 1320$ is not equivalent to a terminating decimal. Without using a calculator, explain whether Lucas is correct or not.
- Lucas is correct as $1320$ has factors of $3$ and $11$
- Lucas is correct as only fractions with a denominator of $10$ terminate
- Lucas is wrong as the fraction simplifies to $1\over20$ which terminates ✓
- Lucas is wrong as the denominator is a multiple of $10$
- Lucas is wrong as $66$ is a multiple of $2$

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The line in a fraction means divide.
Dividing the numerator by the denominator may result in an equivalent terminating decimal.
It can be shown that 1/2, 1/4 and 1/10 have equivalent terminating decimals.
Using a calculator can help investigate fractions which are equivalent to terminating decimals.

Denominators that are multiples of 10 will give a terminating decimal.

Investigate the difference between powers of 10 and multiples of 10. e.g 7/30 and 7/100

Terminating decimals - A terminating decimal is one that has a finite number of digits after the decimal point.