14/11/2018 Starter 10

14/11/2018 Standard Form

STANDARD FORM FOR LARGE NUMBERS 14/11/2018 STANDARD FORM FOR LARGE NUMBERS

14/11/2018 Our decimal number system is based on powers of ten. We can write powers of ten using index notation. 10 = 101 100 = 10 × 10 = 102 1000 = 10 × 10 × 10 = 103 10 000 = 10 × 10 × 10 × 10 = 104 100 000 = 10 × 10 × 10 × 10 × 10 = 105 1 000 000 = 10 × 10 × 10 × 10 × 10 × 10 = 106 …

14/11/2018 For example, the mass of the planet earth is about 5 970 000 000 000 000 000 000 000 kg. We can write this in standard form as a number between 1 and 10 multiplied by a power of 10. 5.97 × 1024 kg A number between 1 and 10 A power of ten

14/11/2018 6 7 5 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Write the number below in standard form 6.754 x 1017 4 3 7 1 0 0 0 0 0 0 0 0 0 0 0 Write the number below in standard form 4.371 x 1014

14/11/2018 . 8 × 107 8 8 × 10 × 10 × 10 × 10 × 10 × 10 × 10 . 0000000 = 80,000,000

14/11/2018 . . 5 273 × 108 5 273 . 5 273 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 . 00000 = 527,300,000

14/11/2018 80 000 000 = 8 × 107 230 000 000 = 2.3 × 108 724 000 = 7.24 × 105 6 003 000 000 = 6.003 × 109 371.45 = 3.7145 × 102

14/11/2018 5 × 1010 = 50 000 000 000 7.1 × 106 = 7 100 000 4.208 × 1011 = 420 800 000 000 2.168 × 107 = 21 680 000 6.7645 × 103 = 6764.5

14/11/2018 300,000 2) 50,000,000 3) 4000 72,000,000 5) 67,000 6) 293,657 7) 46,500,000,000,000 8)100,000,000,000,000 3.0 x 105 5.0 x 107 4.0 x 103 7.2 x 107 2.93657 x 105 6.7 x 104 4.65 x 1013 1.0 x 1014 9) 5 x 104 10) 7 x 106 11) 1 x 103 12) 3.4 x 102 13) 5.67 x 107 14) 4.73 x 102 15) 8.3865676 x 105 16) 2.0003 x 104 50,000 7,000,000 1,000 340 56,700,000 473 838,656.76 20,003

STANDARD FORM FOR SMALL NUMBERS 14/11/2018 STANDARD FORM FOR SMALL NUMBERS

14/11/2018 Any number raised to the power of 0 is 1, so 1 = 100 Decimals can be written using negative powers of ten 0.1 = = = 10-1 1 10 101 0.01 = = = 10-2 1 102 100 0.001 = = = 10-3 1 103 1000 0.0001 = = = 10-4 1 10000 104 0.00001 = = = 10-5 1 100000 105 0.000001 = = = 10-6 … 1 1000000 106

14/11/2018 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2 6 Write the number below in standard form 4.26 x 10-15 0 . 0 0 0 0 0 0 0 0 0 0 5 8 3 Write the number below in standard form 5.83 x 10-11

EXAMPLE: Write the following number in standard form: 0.000045 14/11/2018 EXAMPLE: Write the following number in standard form: 0.000045

14/11/2018 EXAMPLE: Write the following number in standard form: 0.000 000 000 075 32

14/11/2018 . 4 x 10-3 4 4 x 10-1 x 10-1 x 10-1 . 0 00 . = 0 004

14/11/2018 . . 2 35 2 35 x 10-4 2.35 x 10-1 x 10-1 x 10-1 x 10-1 . 0 000 . = 0 000235

14/11/2018 0.0006 = 6 × 10-4 0.00000072 = 7.2 × 10-7 0.0000502 = 5.02 × 10-5 0.0000000329 = 3.29 × 10-8 0.001008 = 1.008 × 10-3

14/11/2018 8 × 10-4 = 0.0008 2.6 × 10-6 = 0.0000026 9.108 × 10-8 = 0.00000009108 7.329 × 10-5 = 0.00007329 8.4542 × 10-2 = 0.084542

14/11/2018 1) 0.003 2) 0.00005 3) 0.01 4) 0.0045 5) 0.000285 6) 0.000000786 7) 0.000002 8) 0.0902 9) 0.9 3 x 10-3 5 x 10-5 1 x 10-2 4.5 x 10-3 2.85 x 10-4 7.86 x 10-7 2 x 10-6 9.02 x 10-2 9 x 10-1 10) 2 x 10-3 11) 4 x 10-5 12) 4.2 x 10-4 13) 3.64 x 10-5 14) 8.412 x 10-1 15) 5.0 x 10-6 16) 9 x 10-8 0.002 0.00004 0.00042 0.0000364 0.8412 0.000005 0.00000009

Let’s Bring it all together with some spaceships 14/11/2018 Let’s Bring it all together with some spaceships

14/11/2018 STANDARD FORM QUIZ! Non calc questions

14/11/2018 Write 4,000,000,000 in standard form

14/11/2018 Write 36,000 in standard form

14/11/2018 Write 14,300,000 in standard form

14/11/2018 Write 0.0006 in standard form

14/11/2018 Write 0.00000025 in standard form

Ordering standard form 14/11/2018 Ordering standard form

14/11/2018 Write these numbers in order from smallest to largest: 5.3 × 10-4, 6.8 × 10-5, 4.7 × 10-3, 1.5 × 10-4. Write these numbers in order from smallest to largest: 4.2 × 107, 1.6 × 106, 3.4 × 106, 7.8 × 105. Write these numbers in order from smallest to largest: 1.8 × 10-2, 6.2 × 10-1, 2.5 × 102, 5.2 × 103.

CALCULATIONS IN STANDARD FORM 14/11/2018 CALCULATIONS IN STANDARD FORM

2 × 103 × 3 × 104 2 × 104 + 3 × 105 = 6 × 107 7.2 × 103 - 3.4 × 104 8 × 107 2 × 103 = 4 × 104

14/11/2018 1) 2 × 103 × 3 × 105 2) 4 × 107 × 1 × 10-2 3) 8 × 105 4) ( 6 × 103)2 6 × 108 4 × 105 4 × 10-2 3.6 × 107 2 × 107 5) 5 × 108 + 7 × 107 6) 8 × 10-4 - 9 × 10-5 7) 400,000 × 2 × 10-3 8) 9 × 10-4 ÷ 0.003 5.7 × 108 7.1 × 10-4 8 × 102 3 × 10-1

14/11/2018 Using a calculator with standard form Complete calculations as usual Use this button to type in standard form numbers Make sure that you INTERPRET the answer correctly, and give your result in the form required by the question × 10 𝑥

14/11/2018 Use a calculator, give answers in standard form Use a calculator, give answers in ordinary form 1) 800,000 × 350,000,000 2) 3 × 105 + 7 × 104 0.0000004 0.00009 7.0 × 1020 4.1 × 109 3) 5.6 × 107 × 60,000 4) 800,000,000,000,000,000 3.2 × 10-5 0.0000000000002 1.1 × 1017 4.0 × 1030 5) (2 × 106)5 6) (-3.4 × 10-3)-2 3.2 × 1031 8.7 × 104 7) 4 × 103 + 5 × 103 8) 0.000004 × 0.00003 3 × 10-2 6 × 10-8 300,000 0.002 9) 8.4 × 10-7 10) (2 × 105)-1 2.1 × 10-3 400,000,000,000,000 0.0004 125,000,000

14/11/2018 STANDARD FORM RECAP

14/11/2018 STANDARD FORM QUIZ! Non calc questions

14/11/2018 Add together 4.2 x 104 and 7.3 x 105

14/11/2018 Multiply 3 x 105 and 2.5 x 107

14/11/2018 Work out (4 x 108) ÷ (5 x 102)

Let’s have a go at the booklet questions 14/11/2018 Let’s have a go at the booklet questions