13 (a) (i) Write \( \frac{1}{3} \) as a recurring decimal - OCR - GCSE Maths - Question 13 - 2019 - Paper 1
Question 13
13 (a) (i) Write \( \frac{1}{3} \) as a recurring decimal.
(ii) Write \( \frac{1}{30} \) as a recurring decimal.
(b) Simplify fully by rationalising the denominato... show full transcript
Worked Solution & Example Answer:13 (a) (i) Write \( \frac{1}{3} \) as a recurring decimal - OCR - GCSE Maths - Question 13 - 2019 - Paper 1
Step 1
(i) Write \( \frac{1}{3} \) as a recurring decimal.
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Answer
The fraction ( \frac{1}{3} ) can be expressed as a decimal by performing the division:
[ \frac{1}{3} = 0.3333... = 0.3\overline{3} ]
Thus, the answer is ( 0.3\overline{3} ).
Step 2
(ii) Write \( \frac{1}{30} \) as a recurring decimal.
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Answer
To convert ( \frac{1}{30} ) into a decimal, we divide 1 by 30:
[ \frac{1}{30} = 0.0333... = 0.0\overline{3} ]
Therefore, the answer is ( 0.0\overline{3} ).
Step 3
Simplify fully by rationalising the denominator: \( \frac{20}{\sqrt{5}} \)
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Answer
To rationalise the denominator, multiply both the numerator and the denominator by ( \sqrt{5} ):
