What you need to know
Convert recurring decimals to exact fractions using algebra. In an exam, identify what information you have before choosing a method. Write each stage clearly so you can check your reasoning as well as your arithmetic.
Worked example
Let x = 0.272727… Then 100x = 27.272727… Subtract: 99x = 27, so x = 27/99 = 3/11.
Method you can repeat
- Identify the structure. Mark the values, variables or relationships the question gives you.
- Choose the rule. Write the relevant equation or relationship before substituting numbers.
- Work accurately. Keep exact values where appropriate and show enough algebra to recover from a calculator slip.
- Check the result. Substitute back, estimate, or ask whether the size and sign of the answer make sense.
Common mistake
Quick practice
Try a fresh question without looking back at the worked example. State the rule you are using first, then complete the calculation and check your answer. GradeRealm's interactive practice provides varied questions so the method becomes reliable rather than memorised from one example.
Exam technique
Show the mathematical relationship before calculator work, keep units attached to measurements, and avoid rounding until the final step unless the question tells you otherwise. If the question says “show that”, your working must connect the information given to the stated result.