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14 (a) Without using a calculator, show that 0.19 can be written as \( \frac{19}{99} \) - OCR - GCSE Maths - Question 14 - 2018 - Paper 6
Question 14
14 (a) Without using a calculator, show that 0.19 can be written as \( \frac{19}{99} \). (b) Explain how \( \frac{19}{99} = 0.19 \) can be used to find \( \frac{19}... show full transcript
Worked Solution & Example Answer:14 (a) Without using a calculator, show that 0.19 can be written as \( \frac{19}{99} \) - OCR - GCSE Maths - Question 14 - 2018 - Paper 6
Step 1
Without using a calculator, show that 0.19 can be written as \( \frac{19}{99} \)
Answer
Let ( x = 0.191919... ) (the repeating decimal).
Multiply both sides by 100: [ 100x = 19.191919... \ ] Now subtract the original equation from this: [ 100x - x = 19.191919... - 0.191919... \ ] This simplifies to: [ 99x = 19 \ ] Therefore, [ x = \frac{19}{99}\ ] Thus, we have shown that 0.19 can be expressed as ( \frac{19}{99} ).
Step 2
Explain how \( \frac{19}{99} = 0.19 \) can be used to find \( \frac{19}{990} \) as a decimal and write down its value.
Answer
To find ( \frac{19}{990} ), we can use the fact that ( \frac{19}{99} = 0.19 ).
From ( \frac{19}{990} ): [ \frac{19}{990} = \frac{19}{99} \cdot \frac{1}{10} \ ] This indicates that ( \frac{19}{990} = 0.19 \div 10 = 0.019 ).
Thus, the value of ( \frac{19}{990} ) as a decimal is 0.019.