1. Produced by MEI on behalf of OCR © OCR 2013 Introduction to Quantitative Methods Standard Form

2. Produced by MEI on behalf of OCR © OCR 2013 This table shows the number of visitors to four tourist attractions … Blackpool tourist information service claimed it had more visitors than the other three added together How do you know if this is true? Blackpool Pleasure Beach6·2 million Edinburgh Castle1 153 000 Alton Towers4·07 x 10 5 Madame Tussauds2·6 million

3. Produced by MEI on behalf of OCR © OCR 2013 Revision of Powers Powers are useful for writing large numbers easily 10 3 =10 x 10 x 10 = 1000 10 7 = 10x10x10x10x10x10x10 = 10000000 3 zeroes

4. Produced by MEI on behalf of OCR © OCR 2013 Powers of ten http://www.powersof10.com/film http://www.powersof10.com/film

5. Produced by MEI on behalf of OCR © OCR 2013 Powers of 10 ThousandHundredTenUnitTenthsHundredthThousandth 10001001010.10.010.001 1000100101 1000100101 10 3 10 2 10 1 10 0 10 -1 10 -2 10 -3

6. Produced by MEI on behalf of OCR © OCR 2013 Check

7. Produced by MEI on behalf of OCR © OCR 2013 Working with big numbers The distance of the earth from the sun is about 149 million km We can write this as 149 000 000 It is usual to leave a space after every three digits from the right.

8. Produced by MEI on behalf of OCR © OCR 2013 Working with big numbers This makes the numbers easier to read and the zeroes easier to count Three zeroes at the end reads as a thousand Six zeroes at the end reads as a million So 235400000 would be written as 2 354 000 000 and would read as 2 354 million

9. Produced by MEI on behalf of OCR © OCR 2013

10. Writing in Standard Form Ordinary Number Standard Form Write the number 8760000 in standard form Remember if a number is in standard form it must have 1 number before the decimal point So Write the number with the decimal point after the first non zero number In this case 8.76 What do you need to multiply by to make this the number we wanted?

11. Produced by MEI on behalf of OCR © OCR 2013 Writing in Standard Form

12. Produced by MEI on behalf of OCR © OCR 2013 Example – write 2509 in Standard Form x 10

13. Produced by MEI on behalf of OCR © OCR 2013 Practice

14. Produced by MEI on behalf of OCR © OCR 2013 Working with small numbers The size of a Carbon atom is 0.000000022cm – a tiny number How would we write this in standard form? First write the number with the decimal point after the first non zero number This is 2.2 What do you need to multiply this by to get back to the number we want?

15. Produced by MEI on behalf of OCR © OCR 2013 x 0.1

16. Produced by MEI on behalf of OCR © OCR 2013 Writing 0.000675 x 0.1

17. Produced by MEI on behalf of OCR © OCR 2013 Example – write 0.0000924 in Standard Form x 0.1

18. Produced by MEI on behalf of OCR © OCR 2013 Practice

19. Produced by MEI on behalf of OCR © OCR 2013 Changing numbers in Standard Form back to Ordinary numbers

20. Produced by MEI on behalf of OCR © OCR 2013

21. Practice

22. Produced by MEI on behalf of OCR © OCR 2013 Changing small numbers in Standard Form back to Ordinary numbers

23. Produced by MEI on behalf of OCR © OCR 2013 4.87 0.487 0.0487 0.00487 0.000487 0.0000487 Answer 0.0000487

24. Produced by MEI on behalf of OCR © OCR 2013 Practice