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

Starter quiz

A decimal with an infinite repeating pattern of digits is called a __________ decimal.
- fractional
- proper
- recurring ✓
- terminating
Match each decimal given using dot notation to its equivalent decimal.
- $0. \dot 7 \dot 8$
  
  ⇔
  
  $0.78787878...$ ✓
- $0.78 \dot 9$
  
  ⇔
  
  $0.789999999...$ ✓
- $0. \dot{7} 8 \dot {9}$
  
  ⇔
  
  $0.789789789...$ ✓
- $0. \dot 7$
  
  ⇔
  
  $0.77777777...$ ✓
- $0. 7\dot 8 \dot 9$
  
  ⇔
  
  $0.789898989...$ ✓
Select all the fractions which are equivalent to a recurring decimal.
- $\frac{5}{12}$ ✓
- $\frac{6}{24}$
- $\frac{2}{3}$ ✓
- $\frac{9}{15}$
- $\frac{2}{12}$ ✓
Use short division to write $11\over15$ as a decimal.
- $0.73$
- $0.73333333333$
- $0. \dot7 \dot3$
- $0.7 \dot3$ ✓
Lucas uses his calculator to write $7\over18$ as a decimal. His calculator display shows the number $0.3888888889$ . Lucas says, "This shows my fraction terminates." Is Lucas correct? Explain why.
- Yes; Lucas' number has 10 digits after the decimal point so it terminates.
- Yes; the last digit is 9 not 8 so it doesn't repeat. So it must terminate.
- No; all decimals recur eventually.
- No; the calculator only has a 12 digit display, the last 8 is rounded up to 9. ✓
Aisha writes the recurring decimal $0.61\dot6$ as the fraction $\frac{\square}{60}$ . What number should she write in the square? ______
- '37' ✓

Terminating decimals have a ______ number of decimal places.
- 'finite' ✓
Write $0.45$ as a simplified fraction.
- $45\over100$
- $9\over20$ ✓
- $8\over20$
- $9\over25$
The fraction which is halfway between 0.44 and 0.86 is $\square \over 20$ . What number should be written in the square? ______
- '13' ✓
Which of the following are equivalent to $4.135$ ?
- $835\over200$
- $827\over200$ ✓
- $4 \frac{27}{200}$ ✓
- $4 \frac{135}{200}$
Match each decimal to a fraction with the denominator in exponential form.
- $3.4$
  
  ⇔
  
  $\frac{34}{10^1}$ ✓
- $0.34$
  
  ⇔
  
  $\frac{34}{10^2}$ ✓
- $0.00034$
  
  ⇔
  
  $\frac{34}{10^5}$ ✓
- $0.034$
  
  ⇔
  
  $\frac{34}{10^3}$ ✓
Laura writes $6.789 = \frac {6789}{10^ \square}$ . What number should she write in the box to make her statement true? ______
- '3' ✓

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Place value of decimals can be represented with exponentials in the column headings.
Terminating decimals have fraction equivalents.
All terminating fractions can be written with exponential denominator with 10 as the base.

The more decimal places there are, the greater the number.

Pupils can investigate this by looking at the numbers 0.23 and 0.1237 and using a common denominator or 10000.

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