GCSE Error intervals Practice Questions

Interpret the rounded value

$x$ has been rounded to the nearest $10$, so it lies in an interval around $70$.

Find the lower and upper bounds

The boundaries lie exactly half a unit ($5$) either side of $70$.

Write the error interval

Any value from $65$ up to $70$ rounds to $70$, so the lower bound $65$ is included. A value of $75$ would round up to the next value, so $75$ is not included.

Interpret the rounded value

$x$ has been rounded to the nearest $10$, so it lies in an interval around $60$.

Find the lower and upper bounds

The boundaries lie exactly half a unit ($5$) either side of $60$.

Write the error interval

Any value from $55$ up to $60$ rounds to $60$, so the lower bound $55$ is included. A value of $65$ would round up to the next value, so $65$ is not included.

State what you are told

$x$ has been rounded to $1$ decimal place.

Find the size of the rounding unit

This is the place value $x$ was rounded to.

Halve the unit

Each boundary is half a unit from $3.9$.

Lower bound

Any value from $3.85$ up to $3.9$ rounds to $3.9$, so the lower bound $3.85$ is included.

Upper bound

A value of $3.95$ would round up to the next value, so $3.95$ is not included.

Write the error interval

Lower bound with $\le$, upper bound with $<$.

State what you are told

$x$ has been rounded to $2$ significant figures.

Find the rounding unit

The value was rounded to this place value.

Halve the unit

Each boundary is half a unit from $24000$.

Lower bound

Any value from $23500$ up to $24000$ rounds to $24000$, so the lower bound $23500$ is included.

Why the lower bound is included

$23500$ rounds up to $24000$, so it belongs to the interval.

Upper bound

A value of $24500$ would round up to the next value, so $24500$ is not included.

Why the upper bound is excluded

$24500$ rounds up to the next value, so it is left out.

Write the error interval

The boundaries lie exactly half a unit ($500$) either side of $24000$.

Check the boundaries

$23500$ rounds to $24000$; $24500$ rounds to the next value.

State the final answer

Lower bound inclusive, upper bound exclusive.

Write down the formula you need

Area of a rectangle is length times width.

Find the bounds of $l$

$l$ is $9.5$ cm to $1$ dp, so it lies half a rounding unit either side.

Find the bounds of $w$

$w$ is $4.5$ cm to $1$ dp, so it lies half a rounding unit either side.

Decide which bounds to combine

Smallest length and width give the smallest area; largest give the largest.

Work out the upper bound

The largest allowed values give the largest result.

Work out the lower bound

The smallest allowed values give the smallest result.

State the answer

Report the required bound with the correct inequality.

Double-check the arithmetic

Recompute carefully so a slip does not change the bound.

Confirm the correct bounds were chosen

A bound of a calculation comes from the extreme values of each measurement.

Explain the strict inequality

Each measurement is strictly below its upper bound, so the result never quite reaches its upper limit.

State the units

Always attach the correct units to a bound.

Beware the common mistake

Substituting the rounded values gives only an estimate, not a true bound.

Interpret the result

This gives the guaranteed range for the true value.

Check reasonableness

The bound should sit close to the estimate from the rounded values.

Re-read the question

Make sure the reported bound (upper, lower or interval) is the one asked for.