13 (a) Write \( \frac{5}{12} \) as a recurring decimal - OCR - GCSE Maths - Question 13 - 2018 - Paper 1
Question 13
13 (a) Write \( \frac{5}{12} \) as a recurring decimal.
(b) Convert 0.7\overline{6} to a fraction.
Worked Solution & Example Answer:13 (a) Write \( \frac{5}{12} \) as a recurring decimal - OCR - GCSE Maths - Question 13 - 2018 - Paper 1
Step 1
Write \( \frac{5}{12} \) as a recurring decimal.
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Answer
To convert ( \frac{5}{12} ) into a decimal, perform long division:
5 divided by 12 gives 0.416666...
This can be expressed as 0.41\overline{6}, indicating that 6 is the recurring digit.
Thus, the answer is ( 0.41\overline{6} ).
Step 2
Convert 0.7\overline{6} to a fraction.
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Answer
Set ( x = 0.7\overline{6} ).
Multiply by 10 to remove the 7: ( 10x = 7.6\overline{6} ).
Next, multiply by 100 to align the repeating part: ( 100x = 76.6\overline{6} ).
Subtract the first equation from the second: ( 100x - 10x = 76.6\overline{6} - 7.6\overline{6} ).
This simplifies to ( 90x = 69 ), hence ( x = \frac{69}{90} ).
Simplifying ( \frac{69}{90} ) by dividing by 3 gives ( \frac{23}{30} ).
