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

A cube has a side length of 4 cm. What is its volume?

View Question

What is the sum of the first 20 odd numbers?

View Question

If log(100) = 2 and log(10) = 1, what is log(1000)?

View Question

If 5x - 2 = 13, what is the value of x?

View Question

A sum triples in 20 years at simple interest. What is the rate of interest per annum?

View Question

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

View Question

If the probability of an event is 1/4, what is the probability of its complement?

View Question

What is the square root of 144?

View Question

If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

View Question

The area of an equilateral triangle with side length 6 cm is:

View Question