Powers & Roots

1. Powers & Roots Squares, Cubes and Powers (Indices) Square Roots and Cube Roots Large Numbers Scientific Notation www.mathsrevision.com Small Numbers Scientific Notation Scientific Notation using Calculator Compiled by Mr. Lafferty Maths Dept.

2. Starter Questions www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

3. Squaring a Number Learning Intention Success Criteria • To understand what is meant by the term power of a number. • We are learning the term • about powers of a number’. • Be able to calculate powers of a number squares both mentally and using the calculator. www.mathsrevision.com Compiled by Mr. Lafferty Maths Dept.

4. Square of a Number To square a number means to : “Multiply it by itself” Example : 92 means 9 x 9 = 81 www.mathsrevision.com 102 means 10 x 10 = 100 Compiled by Mr. Lafferty Maths Dept.

5. Cube of a Number To cube a number means to : “Multiply it by itself and then itself again” Example : 23 means 2 x 2 x 2 = 8 www.mathsrevision.com 43 means 4 x 4 x 4 = 64 Compiled by Mr. Lafferty Maths Dept.

6. Index of a Number n is called the index number an a is called the base number 25 Example : www.mathsrevision.com 32 means 2 x 2 x 2 x 2 x 2 = Compiled by Mr. Lafferty Maths Dept.

7. NON - CALCULATOR 9 1 0 0 0 -8 2 1 6 2 5 6 1 Mr. Lafferty@mathsrevision.com

8. Area of Square Area of a square is l cm A = l x l = l2 Example : Find the area of a square with length 7cm. www.mathsrevision.com A = l2 = 72 = 49cm2 Compiled by Mr. Lafferty Maths Dept.

9. Special button on the calculator Compiled by Mr. Lafferty Maths Dept.

10. Powers & Roots Now try TJ4+ Ex 10.1 Ch10 (page 64) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

11. Square Root of a Number 92 = 9 x 9 = 81 You now know how to find : We can ‘undo’ this by asking “which number, times itself, gives 81” From the top line, the answer is 9 www.mathsrevision.com This is expressed as : “the SQUARE ROOT of 81 is 9” or in symbols we write : Compiled by Mr. Lafferty Maths Dept.

12. Cube Root of a Number 23 = 2 x 2 x 2 = 8 You now know how to find : We can ‘undo’ this by asking “which number, times itself, times itself again gives 8” www.mathsrevision.com From the top line, the answer is 2 This is expressed as : “the CUBE ROOT of 8 is 2” or in symbols we write : Compiled by Mr. Lafferty Maths Dept.

13. Roots of a Number Example : 42 means 4 x 4 = 16 so √16 = 4 53 means 5 x 5 x 5 = 125 www.mathsrevision.com so 3√125 = 5 Compiled by Mr. Lafferty Maths Dept.

14. NON - CALCULATOR 6 8 1 1 7 4 3 Mr. Lafferty@mathsrevision.com

15. Length of a Square Area of a square is 400cm2 l cm A = l x l = l2 Example : Find the length of the square. www.mathsrevision.com l = √A = √400 l = 20 cm Compiled by Mr. Lafferty Maths Dept.

16. Special button on the calculator Compiled by Mr. Lafferty Maths Dept.

17. Powers & Roots Now try TJ4+ Ex 10.2 Ch10 (page 65) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

18. Starter Questions X www.mathsrevision.com www.mathsrevision.com

19. Scientific Notation Learning Intention Success Criteria • To understand and use the quick method to put large numbers into scientific notation and vice versa. • To show a very quick way of putting a large number in scientific notation very quickly and vice versa. www.mathsrevision.com www.mathsrevision.com

20. Very large numbers! BOOM! How far? www.mathsrevision.com 92 000 000 miles

21. Happy 70th Birthday! How many seconds in 70 years? Very large numbers! SPLAT! www.mathsrevision.com 70 years = 2 200 000 000 seconds!

22. Very large numbers! Dinosaurs roamed the earth 228 million years ago www.mathsrevision.com

23. The point moved 6 places Add the decimal point Between 1 and 10 Conversion Move the point to get a number between 1 and 10 = 8 x 10 6 . 8 000 000 . www.mathsrevision.com

24. The point moved 7 places Add the decimal point Between 1 and 10 A short cut Move the point to get a number between 1 and 10 = 9.2 x 10 7 . 92 000 000 . www.mathsrevision.com 9.2 x 10 7 miles

25. The point moved 9 places Add the decimal point Between 1 and 10 A short cut Move the point to get a number between 1 and 10 = 2.2 x 10 9 . 2 200 000 000 . Happy Birthday: Seconds old! = 2.2 x 10 9

26. The point moved 8 places Add the decimal point Between 1 and 10 A short cut Move the point to get a number between 1 and 10 = 2.28 x 10 8 228 000 000 . . www.mathsrevision.com = 2.28 x 10 8 years old

27. Standard Form = 3 x 10 4 (1) 30 000 (2) 700 000 (3) 5 300 (4) 470 000 (5) 9 500 000 (6) 18 300 000 (7) 329 000 (8) 2 560 000 (9) 12 000 000 000 (10) 9 990 000 = 7 x 10 5 = 5.3 x 10 3 = 4.7 x 10 5 = 9.5 x 10 6 = 18.3 x 10 7 www.mathsrevision.com = 3.29 x 10 5 = 2.56 x 10 6 = 1.2 x 10 10 = 9.99 x 10 6

28. The point moves 7 places Zeros after the point aren’t needed. Changing back 8.6 0000000 . =86 000 000 8.6 x 10 7 = www.mathsrevision.com Hint: Add 7 zeros, although you probably won’t need them all.

29. The point moves 5 places Zeros after the point aren’t needed. Changing back 3.46 x 10 5 = 3.46 00000 . =346 000 www.mathsrevision.com Hint: Add 5 zeros, although you probably won’t need them all.

30. Changing back (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) = 600 000 = 8 000 = 650 000 = 120 000 000 = 3 710 000 www.mathsrevision.com = 33 000 = 7 910 000 = 55 500 000 = 10 500 = 3 033 000 000

31. Powers & Roots Now try TJ4+ Ex 10.3 Ch10 (page 65) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

32. Starter Questions www.mathsrevision.com www.mathsrevision.com

33. Scientific Notation Learning Intention Success Criteria • Know how to change very small numbers into scientific notation and how to do the reverse process. • To understand how to change very small numbers into Scientific Notation and vice versa. www.mathsrevision.com www.mathsrevision.com

34. Very small numbers! www.mathsrevision.com How wide is an atom? 0.000 000 000 1 metres wide!

35. The point moved 10 places. Negative sign for small numbers. Standard Form for small numbers Move the point to get a number between 1 and 10 = 1 x 10 -10 . 0.000 000 000 1 www.mathsrevision.com Scale of SMALL Numbers

36. The point moved 7 places. Negative sign for small numbers. Standard Form for small numbers Move the point to get a number between 1 and 10 = 7.6 x 10 -7 . 0.000 000 76 www.mathsrevision.com

37. The point moved 6 places. Negative sign for small numbers. Standard Form for small numbers Move the point to get a number between 1 and 10 = 1.93 x 10 -6 0.000 001 93 . www.mathsrevision.com

38. Standard Form for small numbers (1) 0. 000 3 (2) 0.000 07 (3) 0.000 45 (4) 0.003 4 (5) 0. 000 724 (6) 0.000 000 494 (7) 0.000 095 (8) 0.000 000 098 (9) 0.000 1 03 (10) 0.000 000 000 66 www.mathsrevision.com

39. -3 so remember to move point left for small numbers. Changing back small numbers Hint: Add 3 zeros to the left of the number. 2 x 10 -3 = 2 000 . . www.mathsrevision.com = 0.002

40. -5 so remember to move point left for small numbers. Changing back small numbers Hint: Add 5 zeros to the left of the number. . 8.6 x 10 -5 = 8 6 00000 . www.mathsrevision.com = 0.000086

41. -6 so remember to move point left for small numbers. Changing back small numbers Hint: Add 6 zeros to the left of the number. 5.16 x 10 -6 = . 5 16 000000 . www.mathsrevision.com = 0.000 00516

42. Changing back small numbers (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) = 0.000 5 = 0.000 09 = 0.005 8 = 0.000 000 62 = 0.000 006 45 www.mathsrevision.com = 0.000 000 53 = 0.000 009 17 = 0.002 12 = 0.000 020 3 = 0.000 000 006 032

43. Powers & Roots Now try TJ4+ Ex 10.4 Ch10 (page 68) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

44. Scientific Notation Interactive Calculator Lesson www.mathsrevision.com www.mathsrevision.com

45. Powers & Roots Now try TJ4+ Ex 10.5 Ch10 (page 70) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.