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

What is the value of log₃(27)?

View Question

The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

View Question

What is the sum of the first 20 odd numbers?

View Question

A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

View Question

If the product of two numbers is 120 and their sum is 26, what are the numbers?

View Question

A number is increased by 20% and then decreased by 20%. What is the net change?

View Question

What is the probability of drawing a king from a standard deck of 52 playing cards?

View Question

A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

View Question

A car covers a distance of 150 km in 2.5 hours. What is its average speed?

View Question

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

View Question