Key words: Square Triangle trapezium My Learning Outcome… I will learn… How to round to whole numbers , decimal places and significant figures. I will apply my learning by… Rounding . I will evaluate my learning by… Explaining to your partner how to round to 1 significant figure? L4 Rounding to nearest 10 or 100. L5 Rounding to decimal places. L6 Rounding to significant figures. L7: Be bale to understand standard form. Learning Objective: Application Tasks…

Rounding – to the nearest 10 Learn L 4 Rounding – to the nearest 10 4 8 3 2 4 8 3 7 1 9 5 5 or more? 5 or more? 5 or more? No Yes Yes 4 8 3 0 4 8 4 0 2 0 0

Rounding – to the nearest 100 L 4 Rounding – to the nearest 100 Apply 1 5 8 2 3 1 5 8 7 2 8 9 5 or more? 5 or more? 5 or more? No Yes Yes 1 5 8 2 0 0 5 9 0 0 1 0 0 Copy & complete this table: Number To nearest 10 To nearest 100 To nearest 1000 37 521 274 503 7 630 918 9 875 452 37520 37500 38000 274500 274500 275000 Your Turn 7630920 7630900 7631000 9880 9900 10000 450 500

Rounding to 1 Decimal Place (1DP) Learn 4 . 8 3 2 5 4 . 8 4 2 5 4 . 8 5 2 5 or more? 5 or more? 5 or more? No No Yes 4 . 8 4 . 8 4 . 9 4 . 8 7 5 . 2 6 7 1 4 1 . 9 6 7 5 or more? 5 or more? 5 or more? Yes Yes Yes 4 . 9 5 . 3 2 . 0

Rounding to Decimal Places: 2DP Learn 4 . 8 3 2 5 4 . 8 4 6 4 . 8 5 9 5 1 5 or more? 5 or more? 5 or more? No Yes Yes 4 . 8 3 4 . 8 5 4 . 8 6 1 . 6 9 4 9 5 . 2 6 7 1 1 . 8 9 7 5 or more? 5 or more? 5 or more? No Yes Yes 1 . 6 9 5 . 2 7 1 . 9 0

Rounding to Decimal Places: 3DP Learn 4 . 8 3 2 5 4 . 8 4 6 2 4 . 8 5 9 5 5 or more? 5 or more? 5 or more? Yes No Yes 4 . 8 3 3 4 . 8 4 6 4 . 8 6 0 1 . 6 9 4 2 5 . 2 6 2 7 1 . 9 9 9 9 5 or more? 5 or more? 5 or more? No Yes Yes 1 . 6 9 4 5 . 2 6 3 2 . 0 0 0

Rounding to Decimal Places Apply 1DP 2DP 3DP 4 . 8 5 2 1 . 6 9 4 9 5 . 2 6 2 7 5 or more? 5 or more? 5 or more? Yes No Yes 4 . 9 1 . 6 9 5 . 2 6 3 Copy & complete this table: Number To 1DP To 2DP To 3DP 63.4721 87.6564 149.9875 3.54029 0.59999 63.5 63.47 63.472 87.7 87.66 87.656 Your Turn 150.0 149.99 149.988 D 3.5 3.54 3.540 0.6 0.60 0.600

Significant Figures: Important Zeros in Numbers L6 Learn Significant Figures: Important Zeros in Numbers 5 2 a. Which zeros matter? Are there any we could get rid of and still have the same value? 5 . 2 b. . 5 c. 2 . 5 d. When dealing with Significant Figures, you need to keep any zeros that tell us the value of a number

Rounding to 1 Significant Figure (1SF) L6 Rounding to 1 Significant Figure (1SF) Learn 0 . 0 7 6 5 0 . 0 0 1 2 1 . 0 0 9 5 5 or more? 5 or more? 5 or more? Yes No No 0 . 0 8 0 . 0 0 1 1 2 4 1 5 8 7 7 5 5 or more? 5 or more? 5 or more? No Yes Yes 2 0 0 6 0 0 8 0

Rounding to 2 Significant Figure (2SF) L6 Rounding to 2 Significant Figure (2SF) Learn 1 4 7 2 1 . 4 2 7 9 0 . 0 5 3 5 5 or more? 5 or more? 5 or more? Yes No Yes 1 5 0 0 1 . 4 0 . 0 5 4 4 2 7 2 8 2 0 4 4 7 8 0 . 0 6 9 6 5 or more? 5 or more? 5 or more? Yes No Yes 4 3 0 0 0 2 0 0 0 0 0 0 . 0 7 0

Rounding to 3 Significant Figure (3SF) L6 Rounding to 3 Significant Figure (3SF) Learn 0 . 0 2 6 7 1 3 . 2 9 4 9 3 4 7 2 8 5 or more? 5 or more? 5 or more? No No No 0 . 0 2 6 7 3 . 2 9 3 4 7 0 0 1 3 7 9 8 9 7 4 9 7 8 1 2 . 0 6 9 5 or more? 5 or more? 5 or more? Yes Yes Yes 1 3 8 0 0 9 7 5 0 0 0 1 2 . 1

Rounding to Significant Figures Apply 1SF 2SF 3SF 0 . 0 7 6 5 4 2 7 2 8 1 2 . 0 6 9 5 or more? 5 or more? 5 or more? Yes Yes Yes 0 . 0 8 4 3 0 0 0 1 2 . 1 Copy & complete this table: Number To 1SF To 2SF To 3SF 6.3528 34.026 0.005708 150.932 0.00007835 6.35 6.4 6 34.0 34 30 Your Turn 0.00571 0.0057 0.006 C 151 150 200 0.0000784 0.000078 0.00008

(Use the worksheet “powers of ten” for further explanation) You need to understand about powers of 10. Try these to test your previous knowledge. Learn 105 10-1 102 103 101 10-2 106 10-3 Remember this? 100 104 (Use the worksheet “powers of ten” for further explanation)

149 000 000 km 0.000 000 2 mm Standard Form is used a lot in maths and Learn Standard Form is used a lot in maths and science as a convenient way of writing very large, or very small numbers for example: The distance from the earth to the sun is 149 000 000 km huge! A hydrogen atom has a diameter of about 0.000 000 2 mm microscopic!

Learn Let’s deal with large numbers first. Look at how these numbers have been broken down: = 5 × 100 5000 = 5 × 1 000 50 000 = 5 × 10 000 = 5 × 102 = 5 × 103 = 5 × 104 you know how to write these as powers of 10

Learn What about these? = 5.5 × 102 550 5 500 55 000 = 5.5 × 100 = 5.5 × 1 000 = 5.5 × 103 = 5.5 × 10 000 = 5.5 × 104

Put these numbers into standard form: Learn Put these numbers into standard form: 4 000 = 4 × 103 = 4.5 × 102 = 5.5 × 104 = 3.5 × 103 = 7.5 × 105 6 000 = 6 × 103 = 4 × 102 = 8 × 104 = 9 × 103 = 4 × 105 450 400 55000 80 000 3500 9 000 750 000 4 00 000

× a number between 1 a power and 10 of ten but not including 10 Learn Standard form is: a number between 1 and 10 × a power of ten but not including 10 positive or negative

Now try writing these numbers in standard form: Apply Now try writing these numbers in standard form: = 5 × 106 = 5.5 × 106 = 5.25 × 106 = 5.1 × 106 = 5.156342 × 106 5 000 000 5 500 000 5 250 000 5 100 000 5 156 342

Reverse! Change each of these numbers Learn Reverse! Change each of these numbers to an ordinary number 2.8 × 101 9.9 × 1010 7.1 × 104 3.97 × 102 8.172 × 102 6 × 102 2 × 103 5 × 107 9 × 108 3.7 × 109

The next stage is to write very Learn The next stage is to write very small numbers, i.e. numbers less than 1 Check that you understand about negative powers of 10 0.001 = 0.1 = 1 = 10-1 10 0.01 = 0.0001 = 0.00001 =

Apply Write in standard form: 0.007 0.04 0.000 000 005 0.0234 0.000 002 3 0.006 7 0.000 000 002 34 0.3 0.000 045

Change to small numbers Apply 3.5 × 10-1 4.5 × 10-4 7.2 × 10-5 6.1 × 10-3 1.17 × 10-10

Change each of these to a large or small number: Apply 1.115 × 104 1.412 × 10-3 7.2 × 101 9.01 × 10-2 1.17 × 106 5.5 × 10-6 6.5 × 10-8 3.2 × 105 2.9 × 102 3.167 × 10-11

How do you round to the nearest Significant figure? Evaluate