# 2.1 Rounding up or down after division

After carrying out a calculation you may not have an answer that is suitable.

For example, you are packing items and need to pack 100 items into boxes of 12. After performing the calculation 100 ÷ 12 you arrive at an answer of 8.3333.

This is not particularly helpful as you cannot have 8.3333 boxes. Therefore, you need to round this answer up to 9 boxes. You cannot round down to 8 boxes since some of the items would not get packed.

In other situations, you may need to round an answer down. If you were cutting a length of wood that is 2 m (200 cm) long into smaller pieces of 35 cm you would initially do the calculation 200 ÷ 35. This would give an answer of 5.714…. As you will only actually be able to get 5 pieces of wood that are 35 cm long, you need to round your answer of 5.714 down to simply 5.

**Note:** The three full stops used in the answer above (5.714…) is a character called an ellipsis. In maths it is used to represent recurring decimal numbers so you don’t have to display them all.

## Activity 3: Dividing and rounding

Decide whether the following calculations need to be rounded up or down after calculation of the division sum.

- Apples are being packed into boxes of 52. There are 1500 apples that need packing. How many boxes are required?
- A bag of flour contains 1000 g. Each batch of cakes requires 150 g of flour. How many batches can you make?
- A child gets £2.50 pocket money each week. They want to buy a computer game that costs £39.99. How many weeks will they need to save up in order to buy the game?
- A length of copper pipe measures 180 cm. How many smaller pieces that each measure 40 cm can be cut from the pipe?

### Answer

- 1500 ÷ 52 = 28.84 which must be rounded up to 29 boxes.
- 1000 ÷ 150 = 6.666 which must be rounded down to 6 batches.
- £39.99 ÷ £2.50 = 15.996 which must be rounded up to 16 weeks.
- 180 ÷ 40 = 4.5 which must be rounded down to 4 pieces.