rounding

What is rounding? Rounding is a way of simplifying numbers. If the driveway of a house is 5 metres and 7 cm long we would usually just say it is 5 m long. Saying it's 5 m long will be close enough most of the time. Here is another example. The picture shows a stick of rock next to a ruler. The ruler has only got the 10 cm points marked on it. We can't see exactly how long the rock is. But we can see to the nearest 10 cm. The end of the rock is close to the 20 cm mark. So we say that the rock is 20 cm long to the nearest 10 cm. What about this longer stick. How long is it to the nearest 10 cm? It is closer to 30 cm than 20 cm. So we say it is 30 cm long to the nearest 10 cm. Rounding numbers to the nearest 10 means finding which 10 they are nearest to. Rounding a number to the nearest hundred or to the nearest thousand can be done in the same kind of way. Rules for rounding Example A stick of rock is 27 cm long. How long is it to the nearest 10 cm? Answer 27 cm is between 20 cm and 30 cm. So 27 cm will get rounded to either 20 cm or 30 cm. To get the right answer we need to decide whether 27 is nearer to 20 or 30. You can see from the picture that it is closer to 30.So 27 cm is rounded up to 30 cm.So the stick of rock is 30 cm long when we measure to the nearest 10 cm. For the same reasons 26, 27, 28 and 29 all get rounded up to 30.And 21, 22, 23 and 24 all get rounded down to 20What about 25? It's exactly half way between 20 and 30. It has to be rounded one way or the other. The rule that everyone usually follows is that 25 gets rounded up to 30. The Rules In this way we get the rules about rounding up and down.1, 2, 3 and 4 get rounded down 5, 6, 7, 8 and 9 get rounded up These rules work for all numbers, whether you are using tens, hundreds or thousands (or anything else). Rounding tens, hundreds and thousands Rounding a number is another way of writing a number approximately. We often don't need to write all the figures in a number, as an approximate one will do. For a population of 27 653 the number is large and will change daily. It is better to round up and say 28 000. Rounding to the nearest ten To round a number to the nearest 10, you have to decide if the number is nearest to 10, 20 30 etc. To do this you follow a rule. Is 37 nearer to 30 or to 40? As the unit figure is 7, you round up to 40. Rounding to the nearest 10 can help you estimate the cost of your shopping. Rounding to the nearest hundred To round a number to the nearest 100, you have to decide if the number is nearest to 100, 200, 300 etc. The rule is the same as for rounding to the nearest 10, but this time look at the tens figure. Is 236 nearer to 200 or to 300? As the tens figure is 3, you round down to 200. Rounding to the nearest 100 can help you estimate your yearly spending on rent or mortgage. Rounding to the nearest thousand To round a number to the nearest 1 000, you have to decide if the number is nearest to 1 000, 2 000, 3 000 etc. Follow the rules as above now looking at the hundreds figure. Is 8 572 nearer to 8 000 or to 9 000? As the hundreds figure is 5, follow the rule and round up to 9 000.When a figure is halfway between two hundreds, the rule is to round up. Rounding to the nearest 1 000 can help you estimate the number of people who attended a pop concert or football match. Example If 43 715 tickets were sold for a football match, that number could be rounded to the nearest ten, hundred or thousand: rounding 43 715 to the nearest 10 would give 43 720 rounding 43 715 to the nearest 100 would give 43 700 rounding 43 715 to the nearest 1,000 would give 44 000. Estimating using rounding We can use rounding numbers to get a rough idea or an estimate. An estimate might be a little more or a little less than the actual amount.By carrying out an estimate we can check that the answers to problems are sensible. If you were buying 9 identical shirts for the school's sports team that cost £7.80 each, to get a rough idea of the total cost you could round up £7.80 to £8.00. You could also round up 9 shirts to 10 shirts. Your calculation would then be10 x £8.00 = £80.00 The actual cost would be9 x £7.80 = £70.20 Notice that the actual cost of £70.20 is a little less than our £80.00 estimate. This is because we rounded up. When using a calculator it is a good idea to estimate the answer first in case you make keying errors. Example To estimate the cost of 11 pens at 95p each, you could round down 11 to 10 pens and round up 95p to £1.00 The estimated cost would then be10 x £1.00 = £10.00 Key words for rounding and estimating Here are some words that you'll come across when rounding and estimating. For example with the sum:197 – 50 = 147 Rounding To write a number to a given amount of accuracy.      Rounding 197 to the nearest 100 would be 200. Estimate To give a rough answer that may be a little less or a little more than the actual result.      To estimate 197 – 50 you may instead work out 200 – 50 to give an estimate of 150. Approximate An answer that is not exactly correct but is close enough to be useful in working out a sum.      To approximate 197 – 50 you may instead work out 200 – 50 to give an estimate of 150. To the nearest.. rounding off.. A guide to how accurate your rounding needs to be.      Rounding 197 to the nearest 100 would be 200.      Rounding off 147 to the nearest 10 would be 150. Actual The correct answer to a sum.      The estimate of 197 – 50 is 150. The actual answer is 147.