## Approximation and Estimation

Numbers often need shortening or approximating.

 According to my calculator I have scored an average of1.214285714 tries each game this season! When making calculations or taking measurements, approximations often have to be made. Our rugby playing friend would sound silly so he should say that he had scored just over one try per game.

Numbers can be approximated or rounded to the nearest whole number or nearest hundred etc. or to a certain number of decimal places (often called dec. pl. or d.p.).

Both methods involve the process of 'rounding off'.

### Rounding

The general rule is that if a number is below half way it is rounded DOWN and if it is above halfway it is rounded UP.

 Type of rounding Example Diagram To the nearest whole number Round 3.4 to the nearest whole number. Answer = 3 From the diagram, 3.4 is closer to 3 than it is to 4. To the nearest thousand Round 2680 to the nearest thousand, Answer = 3000 From the diagram, 2680 is closer to 3000 than it is to 2000. To the nearest tenth Round 0.86 to the nearest tenth. Answer = 0.9 From the diagram, 0.86 is closer to 0.9 than it is to 0.8.

If a number is EXACTLY halfway between, the number is rounded UP.

Decimal Places

When writing a number to a given number of decimal places, the number of decimal places required start at the DECIMAL POINT

• Begin by counting the digits from the decimal point.
• Then, if the next digit is a 5 or above, add 1 on to the last digit.
• If the next digit is below a 5, leave it as it is.
 e.g. 8.54 (to 1 decimal place) 8.5 0.069 (to 2 decimal places) 0.07 5.7487 (to 3 decimal places) 5.749 72.38 (to 1 decimal place) 72.4

### Estimation Before making a calculation or solving a problem, especially when using a calculator, an approximate answer should be obtained. This process helps to eliminate mistakes from incorrect keying and calculator malfunction.

Estimates can be obtained mentally by approximating the numbers in the calculation to 1 or 2 digits (depending on the question).

 Example Answer Calculate 3.1 × 8.9 Make an estimate first. Estimate: 3 × 9 = 27 Accurate (from calculator): 27.59

Applications
a

To have a ride on a helicoptor, my two friends and I have to together weigh less than 250 kg.

I weigh 79.8 kg, and my friends weigh 82.1 kg and 67.6 kg.

Do a quick estimate to see if we can fly! My weight is about 80 kg, and my two friends weights are approximately 80 kg and 70 kg.

The total of our approximate weights
= 80 + 80 + 70
= 230 kg.

We can fly!

b

I only have a \$20 note at the supermarket and I want to buy the following items:

 Pizza \$6.90 6 cans of drink \$7.10 Cheese \$2.30 Video \$4.75

Do a quick estimate to see if I can afford to buy them all.

Estimated costs are:

 Pizza \$7 6 cans of drink \$7 Cheese \$2 Video \$5 Estimated total \$21

So I probably need to change my order!