Rounding

Rounding off according to the context

When we round off numbers, we need to be aware of the context of the problem. This will determine whether we round off, up or down.

When we round off to the nearest 10, we follow the simple rule that numbers with units digits from 1 to 4 are rounded down to the lower ten, while numbers with units digits from 5 to 9 are rounded up to the higher ten.

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However, when we are working in some practical, real-life situations, we must think carefully about what the results of rounding off will be. In other words, the answer must be reasonable so that it is not only correct, but also makes sense in the situation.

For example, South Africa no longer has 1c and 2c coins, so shops need to round off the totals to a 5c value if customers are paying cash. Shops round down, rather than rounding off. So if your total is R 13,69, you would pay R 13,65 in cash. If you pay by credit or debit card however, the totals are not rounded off.

Example 1: Rounding up and down

Question

Answer the following questions and in each case explain why you would round up or down to get a reasonable answer.

  1. Jacolene is catering for a group of 54 people. The muffins are sold in packs of 8. How many packs of muffins must she buy?
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  2. A group of learners is going to the Maropeng Centre at the Cradle of Humankind. There are 232 learners and teachers going on the outing. The school needs to hire buses and each bus can carry 50 passengers.

    1. How many buses should they hire?
    2. How many empty seats will there be?
  3. Ludwe is buying blinds for a large window in his home. Each blind is 100 cm wide. The window is 260 cm wide. How many blinds does he need?
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Answer

  1. Jacolene has to decide whether to round up and buy \(\text{7} \times \text{8} = \text{56}\) muffins, so that there will definitely be enough for each person to have one, or whether it is unlikely that everyone will want a muffin, in which case she can round down to \(\text{6} \times \text{8} =\text{48}\) muffins.
    1. To make sure that no learners are left behind, we have to round the number of seats up to the next 50, so 232 is rounded up to 250, and there must be 5 buses.
    2. There will be 250 - 232 = 18 empty seats.
  2. In this situation, Ludwe will probably round up again, as it would be a problem to have a part of the window exposed, and more acceptable to have the blinds wider than the window width. So he would round up the total width of blinds to 300 cm, so that there would be 3 blinds in total.

Exercise 1: Rounding off in real-life situations

Michael needs 1245 tiles to tile a bathroom. He can only buy tiles in packs of 75.

  1. Should he round the number of tiles up or down to see how many he should buy? Explain.

  2. How many packs should he buy?

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  1. He should round up. If he rounds down he won't have enough tiles to cover the floor!

  2. \(\text{1245} \div \text{75} = \text{16,6}\). So he should buy 17 packs.

A classroom wall is 750 cm long.

  1. How many tables, each 120 cm long, will fit along the wall?

  2. How much space will be left over?

  1. \(\text{750}\text{ cm} \div \text{120}\text{ cm} = \text{6,25}\). So 6 tables will fit along the wall.

  2. \(\text{6} \times \text{120}\text{ cm} = \text{720}\text{ cm}\), so there will be \(\text{750}\text{ cm} - \text{720}\text{ cm}= \text{30}\text{ cm}\) left over.

There are 231 learners in a Grade 10 group. They each need an exercise book, which are sold in packs of 25.

  1. How many packs of books should be ordered?

  2. How many spare exercise books will there be?

  1. \(\text{231} \div \text{25} = \text{9,24}\). 10 packs should be ordered.

  2. \(\text{10} \times \text{25} = \text{250}\). 250 - 231 = 19 spare books.

Julia needs to make 500 hamburgers for a school function. Hamburger patties are sold in packets of 12.

  1. How many packets of patties should she buy?

  2. How many will be left over?

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  1. \(\text{500} \div \text{12} = \text{41,67}\). She should buy 42 packs.

  2. \(\text{42} \times \text{12} = \text{504}\). 504 - 500 = 4 spare patties.

Car parking spaces should be 2,5 m wide. How many parking spaces should be painted in a car park which is 72 m wide?

\(\text{70} \div \text{2,5} = \text{28,8}\). So 28 parking spaces can be painted in the car park.