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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 0.7̅ 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.
Answer
To convert ( \frac{5}{12} ) to a decimal, divide 5 by 12:
- Perform the division: ( 5 \div 12 = 0.416666... )
- Recognizing the repeating pattern, we can express it as: ( 0.41\overline{6} )
Thus, ( \frac{5}{12} ) as a recurring decimal is ( 0.41\overline{6} ).
Step 2
Convert 0.7̅ to a fraction.
Answer
Let ( x = 0.7\overline{6} ).
To eliminate the repeating decimal:
- Multiply both sides by 10 to move the decimal: ( 10x = 7.6\overline{6} )
- Now, subtract the original equation from this new one: [ 10x - x = 7.6\overline{6} - 0.7\overline{6} ] [ 9x = 6.9 ]
- Rearranging gives ( x = \frac{69}{90} ).
- Simplifying the fraction, we divide both the numerator and denominator by 3: ( x = \frac{23}{30} ).
Thus, 0.7̅ as a fraction is ( \frac{23}{30} ).