Rounding Numbers – GCSE Mathematics (Foundation) AQA Revision

Understanding Rounding Numbers

Rounding numbers is a mathematical method used to approximate a number to a nearby or similar number for simplicity.
When rounding, numbers less than half way to the next number typically round down, and numbers equal to or more than half way to the next number round up.
The location to which you are rounding to is called the place value. This place value determines what digit in the number you are rounding.

When rounding to decimal places, consider the digit to the right of the required decimal place.
For example, to round 12.345 to 2 decimal places, you would look at the third decimal digit (which is 5). Since 5 is half way or more, the second decimal digit would round up from 4 to 5, leaving us with 12.35.

Significant figures are digits in a number that contribute to its precision, starting from the first non-zero digit.
When rounding to significant figures, consider the digit to the right of the required significant figure.
For example, to round 456.789 to two significant figures, you would look at the third digit (which is 6). Since 6 is half way or more, the second digit would round up from 5 to 6, giving us 460.

If a decimal is half way or more (0.5 or more), it rounds up to the next whole number. If it’s less than half way (less than 0.5), it rounds down.
For example, 3.57 would round down to 3, while 3.524 would round up to 4.

Only round once: it is a common mistake to round a number twice in the same problem. Always make sure to only round your final answer, and not any intermediate calculations.
Misplacing decimal points: Rounding decimals requires careful placement. Remember that the number of decimal places indicates how many digits there are after the decimal point.
Forgetting place values: When rounding to significant figures, it is important to start from the first non-zero digit on the left.