Estimation and limits of accuracy

• Round to a given number of decimal places or significant figures, or to the nearest 10, 100, 1000.
• Estimate a calculation by rounding each number to 1 significant figure.
• Round a final answer to a sensible degree of accuracy for the context.
• Write down the upper and lower bounds of a rounded value.
• Find upper and lower bounds of sums, differences, products and quotients, e.g. perimeter, area and speed.

Decimal places and significant figures

Look at the digit after the last one you keep: 5 or more rounds up, 4 or less leaves it. Decimal places count from the decimal point. Significant figures count from the first non-zero digit; zeros at the start of a small number are not significant, but you keep place-holding zeros in a large number.

Round each number to 1 significant figure

Round every number to 1 significant figure, then work it out mentally. Show the rounded numbers: that is where the marks are.

The answer must make sense

Give money to the nearest cent, people and buses as whole numbers, and lengths to a sensible precision. When a final answer is not exact and no accuracy is stated, give it to 3 significant figures (angles in degrees to 1 decimal place). Think about whether to round up or down: 230 people need 5 buses of 50, not 4.6 buses.

Half a unit either side

If a value is rounded to the nearest unit u, the true value lies within half a unit either side. The lower bound is included; the upper bound is not (it would round up).

Choose the combination that makes the answer biggest or smallest