Estimation Revision Notes

Rounding to decimal places means adjusting a number so that it has a specified number of digits after the decimal point. This is useful when you want to simplify a number while keeping a certain level of precision.

To round a number to a given number of decimal places, look at the digit immediately after the last decimal place you want to keep. If this digit is 5 or more, increase the last kept digit by 1. If it is less than 5, leave the last kept digit as it is and remove all digits after it.

For example, to round 3.2764 to 2 decimal places: the third decimal digit is 6 (which is greater than 5), so increase the second decimal digit (7) by 1, giving 3.28.

• Identify the digit at the required decimal place.
• Check the next digit to decide whether to round up or down.
• Adjust the last kept digit accordingly and remove digits after it.

Significant figures refer to the number of important digits in a number, starting from the first non-zero digit. Rounding to significant figures is common in scientific and engineering contexts where the precision of measurements matters.

To round a number to a specified number of significant figures, first identify the first non-zero digit. Count the required number of digits from this point. Look at the next digit to decide whether to round up or down, then adjust and remove digits accordingly.

For example, to round 0.0413 to 1 significant figure: the first non-zero digit is 4, the next digit is 1 (less than 5), so keep 4 and replace the rest with zeros or remove them, giving 0.04.

• Locate the first non-zero digit.
• Count the required number of significant figures from this digit.
• Use the next digit to decide rounding up or down.
• Adjust digits and remove or replace trailing digits appropriately.

Estimation involves simplifying numbers to make calculations easier and faster, often by rounding to a convenient level of precision. This is especially useful when an exact answer is not necessary or when checking the reasonableness of a result.

For example, to estimate 5764 to the nearest thousand, look at the hundreds digit (7). Since it is 5 or more, round up the thousands digit (5) by 1, resulting in 6000. This estimate is easier to work with in mental calculations.

Similarly, estimating 41.3 to 1 significant figure involves rounding to 40, which simplifies calculations while maintaining a reasonable approximation.

• Identify the place value or significant figure to round to based on the problem.
• Use rounding rules to simplify the number.
• Use the estimate to perform approximate calculations or checks.

When presenting answers, it is important to round results to a level of accuracy that suits the context. Overly precise answers may be misleading or unnecessary, while too rough rounding can lose important information.

Consider the units involved, the precision of the original data, and the purpose of the calculation. For example, if measuring length to the nearest millimetre, it is sensible to round the final answer to millimetres, not to whole metres.

In exam questions, follow any instructions about rounding. If none are given, use your judgement based on the context and the precision of the data provided.

• Check the precision of the original data.
• Consider the units and context of the problem.
• Round the final answer to a suitable number of decimal places or significant figures.
• Follow any specific instructions given in the question.