Topic Details (Notes format)

How to Convert Repeating Decimals to Fractions

Subject: Mathematics

Book: Maths Mastery

A repeating decimal, such as 0.333... or 0.727272..., can be turned into a fraction using algebraic manipulation. For example, let x = 0.333.... Multiplying by 10 if there is 1 repeating digit, we get 10x = 3.333..., then 10x – x = 3.333... – 0.333... = 3, so 9x = 3, x = 3/9 = 1/3. For 0.727272..., let x = 0.727272..., multiply by 100 to shift two repeating digits: 100x = 72.727272..., subtract x to isolate the repeating part. This skill is crucial in pure math, simplifying exact decimal expansions, or verifying repeating patterns in financial or scientific data analysis.

Practice Questions

If 2a + b = 10 and a - b = 4, what is the value of a?

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What is the sum of the first 10 positive even numbers?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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If x = 3 and y = 4, what is the value of x^2 + y^2?

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If sin(θ) = 0.6 and θ is acute, what is cos(θ)?

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What is the sum of all odd numbers from 1 to 99?

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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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What is the square root of 121?

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If x - y = 5 and x + y = 15, what is the value of x?

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What is the sum of all even numbers between 1 and 50?

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