FRACTIONS, DECIMALS AND PERCENTAGES

Recurring Patterns

Learn the reliable method for recurring patterns, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Decimals use place value to represent tenths, hundredths and thousandths. Recurring Patterns depends on keeping each digit in its correct column.

Picture itSee each decimal digit hold its place
2 · THE METHOD

Follow these steps

  1. Write numbers with decimal points aligned.
  2. Compare using place value, adding zero placeholders if useful.
  3. Estimate first, then check the number of decimal places in the answer.
3 · WORKED EXAMPLES

See the method in action

Example 1

Term n is formed by writing the two-digit block 82 exactly n times after the decimal point. Which term has 6 digits after the decimal point?

  1. Each block has two digits. (6) ÷ 2 = 3, so this is term 3.
Answer: 3
Example 2

The pattern appends 72 each time: 0.72, [missing], 0.727272. Which term is missing?

  1. Append 72 once to 0.72 to get 0.7272.
  2. A further block gives 0.727272.
Answer: 0.7272
4 · ELEVENSPRINT TIP

A useful shortcut

Trailing zeros do not change a decimal's value: 0.7 = 0.70.

5 · COMMON MISTAKES

Watch out for these

Aligning the final digits

Align decimal points, not the right-hand edge of the numbers.

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.