Numeracy · Topic 6 of 6
Rounding
Theory
The Golden Rule: If a question requires you to round your answer, you must write down your unrounded answer from your calculator display first before you write your rounded answer. If you do not write down your unrounded answer first, you will risk losing multiple marks, even if your final rounded answer is completely correct.
1. Decimal Places (d.p.)
When rounding to a specified number of decimal places (you are expected to be able to round to three decimal places), you only consider the number immediately to the right of your cut-off point.
- If the digit is 5 or more, round up.
- If the digit is 4 or less, keep it the same.
- Example: 8.4996 rounded to 3 d.p. is 8.500.
2. Significant Figures (s.f.)
Significant figures begin at the first non-zero digit in a number, reading from left to right.
- Once you find your first significant figure, count along to find the required number of figures, then round.
- You must fill any remaining spaces before the decimal point with placeholder zeroes.
- For numbers less than 1 (e.g., 0.00567), the zeroes at the start are not significant. The first significant figure is the 5.
- Example: 59,208 rounded to 2 s.f. is 59,000.
3. Money Formatting
Decimal answers for financial calculations must always be given to exactly two decimal places, even if the question does not explicitly tell you to round. Writing an answer as £2.5 rather than £2.50 will cost you a mark.
4. Contextual Rounding (Real-Life Situations)
In some real-life situations, a decimal answer makes no logical sense, and you must decide whether to round up or down to the nearest whole number based on the context.
- Rounding Up: If you are calculating how many buses are needed for a trip, or how many packets of seeds are required to cover a lawn, you must round up (e.g., 19.6 buses means you must order 20 buses, because 19 isn't enough).
- Rounding Down: When calculating how many objects fit into a container, you must truncate (round down) to a whole number, because you cannot pack a fraction of an object.
⚠️ Common Examiner Traps
- The "Hidden Unrounded" Trap: This is one of the most common ways candidates drop marks across the entire paper. In multi-mark questions (like compound percentages), one mark is awarded for the unrounded answer, and the final mark is for the rounding. Skipping straight to the rounded answer loses both marks.
- The "Trailing Zero" Trap: When rounding to significant figures, candidates often incorrectly add .0 or .00 to the end of a whole number. For example, rounding 446.586 to 1 s.f. is 400, not 400.0.
- The "Ignoring Context" Trap: Candidates frequently calculate an exact decimal and move on without reading the context. If a question asks "How many complete cakes can be made?", leaving an answer of 42.8 instead of 42 will lose you the final communication mark.
Worked examples
Example 1
A local charity receives a donation of £45,000. They invest the money in an account that pays a compound interest rate of 3.4% per annum. Calculate the value of the investment after 4 years. Give your answer to 3 significant figures. (4 marks)
Step 1: Calculate the decimal multiplier for a 3.4% increase.
Step 2: Apply the multiplier and the power for 4 years.
Step 3: Write down the unrounded answer from the calculator. (Do not skip this!)
Step 4: Round to the first 3 significant figures (the 5, the 1, and the 4). Use zeroes as placeholders for the rest of the whole number.
Example 2
A school is organising a trip to a museum for 334 pupils and 18 teachers. They are hiring coaches for the journey. Each coach holds a maximum of 48 passengers. Calculate how many coaches the school must hire. (3 marks)
Step 1: Calculate the total number of passengers.
Step 2: Divide the total passengers by the capacity of one coach.
Step 3: Make a contextual decision. You cannot hire 0.33 of a coach. 7 coaches would only hold 336 people, leaving people behind. Therefore, you must round up.
Example 3
Convert to a decimal fraction. Round your answer to 3 decimal places. (2 marks)
Step 1: Divide the top number by the bottom number to convert to a decimal, writing down the unrounded display.
Step 2: Look at the 4th decimal digit (the 1) to decide how to round the 3rd digit (the 7). Because it is 4 or less, it stays the same.