Estimation Revision Notes

Rounding to decimal places means adjusting a number so that it has a specified number of digits after the decimal point. To round a number to a certain decimal place, look at the digit immediately after that place. If this digit is 5 or greater, increase the digit in the rounding place by one; if it is less than 5, leave the rounding digit unchanged and remove all digits after it.

For example, to round 9.79 to one decimal place, look at the second decimal digit (9). Since 9 ≥ 5, increase the first decimal digit (7) by one, giving 9.8.

This method is useful when you want to express a number with a fixed number of decimal places, often to match the precision of measurements or to simplify calculations.

• Identify the decimal place to round to.
• Check the digit immediately to the right.
• If digit ≥ 5, round up; if digit < 5, round down.
• Remove digits after the rounding place.

Significant figures represent the number of meaningful digits in a number, starting from the first non-zero digit. Rounding to significant figures involves keeping a specified number of these meaningful digits and adjusting the rest accordingly.

For example, to round 41.3 to 1 significant figure, identify the first non-zero digit (4). The next digit is 1, which is less than 5, so the 4 remains unchanged and the digits after it become zero or are removed, giving 40.

This method is especially useful when dealing with numbers that vary widely in size or when the precision of the number is more important than the exact decimal placement.

• Count significant figures starting from the first non-zero digit.
• Look at the digit immediately after the last significant figure to decide rounding.
• Replace digits after the last significant figure with zeros or remove them if decimal.
• Use significant figures to express precision in measurements and calculations.

Estimation simplifies calculations by replacing numbers with rounded values that are easier to work with mentally or quickly. When estimating, round each number involved to an appropriate level of precision, often to one significant figure, then perform the calculation.

For example, to estimate the value of 41.3 × 2.8, round 41.3 to 40 (1 significant figure) and 2.8 to 3 (1 significant figure). Then multiply 40 × 3 = 120 as an estimate.

Estimation is useful for checking the reasonableness of answers, making quick decisions, or when exact values are not necessary.

• Round each number to a suitable precision (often 1 significant figure).
• Perform the calculation using the rounded numbers.
• Use estimation to check exact calculations or when speed is important.
• Understand that estimation provides approximate results, not exact answers.

The level of accuracy for rounding final results depends on the context of the problem, including the precision of the original data and the purpose of the calculation.

For example, if measurements are given to two decimal places, it is reasonable to round the result to two decimal places. If the problem involves counting objects, rounding to whole numbers is appropriate.

Consider the precision of input data and the significance of digits when deciding how to round results. Over-rounding can lose important information, while under-rounding can give a false impression of accuracy.

• Match the rounding precision to the least precise input data.
• Consider the context and purpose of the calculation.
• Avoid giving more decimal places or significant figures than justified.
• Round intermediate steps only when necessary; round final answers appropriately.