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

Starter quiz

Terminating decimals have a ______ number of digits after the decimal point.
- 'finite' ✓
Without using a calculator, work out the decimal value of $\frac {13}{20}$ . ______
- '0.65' ✓
Select all the fractions that can be written as terminating decimals.
- $\frac {11}{15}$
- $\frac {11}{4}$ ✓
- $\frac {11}{8}$ ✓
- $\frac {11}{50}$ ✓
- $\frac {11}{30}$
Aisha uses her calculator to convert $0.668$ to a fraction. She gets an answer of $\frac {167}{\square}$ . What number should go in the square? ______
- '250' ✓
Match each fraction to its terminating decimal. You can use a calculator for this question.
- $\frac {73}{160}$
  
  ⇔
  
  $0.45625$ ✓
- $\frac {57}{125}$
  
  ⇔
  
  $0.456$ ✓
- $\frac {63}{140}$
  
  ⇔
  
  $0.45$ ✓
- $\frac {2281}{5000}$
  
  ⇔
  
  $0.4562$ ✓
- $\frac {34}{85}$
  
  ⇔
  
  $0.4$ ✓
Sam says that $231 \over 330$ is not equivalent to a terminating decimal. Without using a calculator, explain whether Sam is correct or not.
- Sam is correct as $330$ has factors of $3$ and $11$
- Sam is correct as only fractions with a denominator of $10$ terminate
- Sam is wrong as $330$ is a multiple of $10$
- Sam is wrong as the fraction simplifies to $7\over10$ which terminates ✓

A decimal with an infinite repeating pattern of digits is called a ______ decimal.
- 'recurring' ✓
Match each decimal given using dot notation to its equivalent decimal.
- $0. \dot 1 \dot 2$
  
  ⇔
  
  $0.12121212...$ ✓
- $0. 1 2 \dot 3$
  
  ⇔
  
  $0.123333333...$ ✓
- $0. \dot{1} 2 \dot {3}$
  
  ⇔
  
  $0.123123123...$ ✓
- $0. \dot 1$
  
  ⇔
  
  $0.111111111...$ ✓
- $0. 1\dot 2 \dot 3$
  
  ⇔
  
  $0.123232323...$ ✓
Select all the fractions which are equivalent to a recurring decimal.
- $\frac{1}{3}$ ✓
- $\frac{1}{12}$ ✓
- $\frac{3}{24}$
- $\frac{6}{15}$
- $\frac{10}{12}$ ✓
Use short division to write $8\over15$ as a decimal.
- $0.53$
- $0.53333333333$
- $0.5 \dot3$ ✓
- $0. \dot5 \dot3$
Jacob uses his calculator to write $11\over12$ as a decimal. His calculator display shows the number $0.9166666667$ . Jacob says, "This shows my fraction terminates." Is Jacob correct? Explain why.
- Yes; Jacob's number has 10 digits after the decimal point so it terminates.
- Yes; the last digit is 7 not 6 so it doesn't repeat. So it must terminate.
- No; the calculator only has a 12 digit display, the last 6 is rounded up to 7. ✓
- No; all decimals recur eventually.
Izzy writes the recurring decimal $0.71\dot6$ as the fraction $\frac{\square}{60}$ . What number should she write in the square? ______
- '43' ✓

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Dividing the numerator by the denominator may result in an equivalent recurring decimal.
It can be shown that 1/9, 1/11 and 1/36 have equivalent recurring decimals.
Using a calculator can help investigate fractions which are equivalent to terminating decimals.
Using a calculator can help investigate fractions which convert to recurring decimals.

Converting a fraction to a recurring decimal and then rounding the decimal, gives an accurate answer

The use of fractions is more preferred for accuracy than decimals. e.g 1/3 + 1/3 + 1/3 is not 0.3 + 0.3 + 0.3

Recurring decimals - A recurring decimal is one that has an infinite number of digits after the decimal point.