Estimation and rounding – iGCSE Mathematics OxfordAQA Revision

Estimation means approximating a value that makes sense and is close to the actual value. This skill is essential as it’s often impractical or impossible to calculate an exact answer.
Rounding, also known as Rounding off, is a form of estimation that involves reducing the number of digits in a number while trying to keep its value similar.

Rounding to the nearest whole number: This means converting a decimal into the nearest whole number. For example, if you round 1.6 to the nearest whole number, you’d get 2 because 1.6 is closer to 2 than it is to 1.
Rounding to a certain decimal place: When you’re asked to round a number to a specific decimal place, the digit in the next place determines whether the digit in the place of interest goes up or stays the same. For example, rounding 1.67 to one decimal place gives 1.7 because 7 (in the hundredths place) is greater than or equal to 5.
Rounding to significant figures: A significant figure in a number is a digit (starting from the first non-zero digit on the left) that carries meaning contributing to its precision. When rounding to a certain number of significant figures, one would keep the desired number of figures from the left, adjusting the last kept figure depending on what follows.

If the number next to the digit you’re rounding is 5 or greater, round up. If it’s less than 5, then round down. This is also known as the 5 or more, raise the score. 4 or less, let it rest. rule.
When rounding to significant figures, if the number beyond the last significant figure is 5 followed by non-zero digits, increase the last significant figure by 1.
Be mindful of rounding errors as continuous rounding can lead to inaccuracies. Endeavour to retain as much precision as possible until the final calculation step.
If your result falls exactly in the middle (with 5 as the deciding number), then round to the even number. This is known as Round Half To Even or the Bankers’ Rounding.
A number stays the same when rounded to a larger place value (e.g., thousands are rounded to the same number in tens and hundreds).

Useful for making quick calculations in daily life, such as estimating totals while shopping.
Essential for checking the plausibility of an answer in mathematics problems. For example, by estimating first, one can gauge whether their exact solution is reasonable.
Important in presenting data in a simplified and more understandable format by rounding off to an appropriate number of decimal places or significant figures.

Understand that estimation is not about finding the exact answer. Sometimes people tend to calculate instead of using estimation techniques.
Remember that choice of rounding method can affect the accuracy of future calculations. Ensure to follow appropriate rules for rounding.
Always practise these skills - accuracy in rounding and estimation often comes with practice and familiarity with numbers.