7.3 Rounding and error intervals — Learn

Prerequisites: rounding to decimal places and significant figures.

Before you begin

You should know how to round numbers to a stated number of decimal places or significant figures.

Objectives

• Round to a stated degree of accuracy.
• Write an error interval for a rounded value.
• Interpret interval endpoints in context.

Rounding and intervals

An error interval lists all original values that round to the stated value. If a length rounds to $4.7$ cm to the nearest $0.1$ cm, values start at $4.65$ cm and stop before $4.75$ cm.

The lower endpoint is included because it rounds up to $4.7$. The upper endpoint is excluded because it rounds to $4.8$.

Example 1. A mass is $320$ g to the nearest $10$ g. Give its error interval.

Half of $10$ is $5$. Subtract and add $5$ to the stated value.

Example 2. A time is $12.4$ seconds to the nearest tenth. Give its interval.

Half of $0.1$ is $0.05$.

Watch out. A common error is to include the upper endpoint. For $4.7$ cm to the nearest $0.1$ cm, $4.75$ cm rounds to $4.8$ cm, so write $L<4.75$.

Progress check. A distance is $8.2$ km to the nearest $0.1$ km. Predict the two interval endpoints.

You should now be able to

• round values to a stated degree of accuracy;
• find the half-step around a rounded value;
• write and interpret an error interval with correct inequality signs.