2. vms http://www.mathsisfun.com/fractions.html Year 8 Mathematics Rounding

3. Learning Intentions round a given whole number to the nearest 10, 100, 1000 and so on Be able to identify significant figures round a decimal number to a given number of decimal places or significant figures use rounded numbers to find rough estimates for calculations

4. Rounding Giving the complete number for something is sometimes unnecessary. For example The attendance at a football match might be 23745. But for most people who want to know the attendance figure, an answer of 'nearly 24000', or 'roughly 23700', is fine. We can round off large numbers like these to the nearest thousand, nearest hundred, nearest ten, nearest whole number, or any other specified number.

5. Decimal Places When we do a calculation the answer is not always whole number and often involves decimal places. Sometimes there are too many decimal places to write down. For example: one third = 0.333333…. When we have numbers like this we write a number that is close to the answer. We round to a specific number of decimal places

6. Rounding Decimal Places Numbers can be rounded to 1, 2, 3 or more decimal places. To round a number to a given number of decimal places: look at the number in the next decimal place If it's less than 5, round down If it's 5 or more, round up Round this number to 1 decimal place 2 decimal places

7. Some More examples Rounding to 1 decimal place 4. 8 3 2 5 5 or bigger ? 4.8 4. 8 4 2 5 5 or bigger ? 4.8 3. 9 5 2 5 5 or bigger ? 4.0 No Yes

8. Significant Figures Rounding 12.756 or 4.543 to one decimal place seems sensible, as the rounded figures are roughly equal to the actual value. 12.756 = 12.8 (1 decimal place) 4.543 = 4.5 (1 decimal place) But what happens if you round a very small number to one decimal place? 0.00546 = 0.0 (1 decimal place) 0.00213 = 0.0 (1 decimal place) This is not a useful answer. Another way to find an approximate answer with very small numbers is to use significant figures.

9. Counting Significant Figures Significant figures start at the first non-zero number, so ignore the zeros at the front, but not the ones in between. Look at the following examples:

10. Significant Figures When we approximate whole numbers we may need to insert zeros as required in order to maintain the size of the number Round the following to 3 Significant Figures 5 4 7 2 5 or bigger ? 5 470 No 8 3 7 9 8 5 or bigger ? 83 800 Yes 9 7 4 9 7 8 5 or bigger ? 975 000 Yes

11. Small Numbers Remember the first significant number is the first non-zero digit! Round to 4 sf. 0. 0 1 0 2 3 8 3 5 or bigger ? 0.01024 Yes First non- zero digit.

12. More Examples E.g. Round each of the following: 20947 (1.s.f) 2099 (3.s.f) 3.002 (2.s.f) 0.00692157 (4.s.f)

14. Estimating We can use rounding to estimate the results of calculations This can help us to check our answers To do this we round each number to 1 sf E.g. Estimate a) 3827 x 1.93 b) 34.63 ÷ 5.03 c) 36.8 x 0.81 2.491 d) 0.0237 x 109 1.43 x 1.53