ROUNDING AND ESTIMsddsddsdsddsdATING.pptx

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1. Which number am I? 1 - I have one decimal place 2 - When I’m rounded to the units, I’m the number 4. 3 - I have 2 significant figures 4 - Without my decimal point I’m a prime number.

2. 3.7 or 4.1 or 4.3

3. Which number am I? 1 - I have 1 significant figure. 2 - Without my decimal point I’m a multiple of 4. 3 - I have 2 decimal places 4 - When I’m rounded to the nearest tenth I’m the number 0.1

4. 0.08

5. Lesson 1 Significant Figures

6. Identifying Significant Figures 0.00 5 83 000 Leading zeros In between zeros Nonzero digit Trailing zeros

7. Look at these examples (significant figures - s.f.) How many s.f. do you think each of them have? Write it down in your notebook 0.040 0.36 0.008 230.0 → 2 s.f. → 2 s.f. → 1 s.f. → 6 s.f. → 3 s.f. → 2 s.f. → 3 s.f. 2230.05 120. 120 12,400 → 4 s.f.

8. Identifying Significant Figures 0.00 5 83 000 Leading zeros will never count Nonzero digit and in between zeros will always count Trailing zeros will depend on the situation…. Leading zeros In between zeros Nonzero digit Trailing zeros

9. Trailing zeros will depend on the situation…. 0.040 230.0 120. 120 12,400 Look at these numbers as if they were representing measurements. We will count the s.f. by considering which digits are giving us a precise measurements.

10. Trailing zeros will depend on the situation…. 0.04 230. 120. 120 12,400 Look at these numbers as if they were representing measurements. We will count the s.f. by considering which digits are giving us a precise measurements. These zeros are “optional” which means that if they are written there, it’s because I measured all the way up to their places and I know it’s a zero there, not a 1, 3, 5 or a 8 for example.

11. Trailing zeros will depend on the situation…. 0.040 230.0 120. 12 12,4 00 Look at these numbers as if they were representing measurements. We will count the s.f. by considering which digits are giving us a precise measurements. These zeros are not “optional” which means that we can’t guarantee if they are there just because they have to or because someone really measure all the way up to the units place.

12. Trailing zeros will depend on the situation…. 0.040 230.0 120 . 120 12,400 Look at these numbers as if they were representing measurements. We will count the s.f. by considering which digits are giving us a precise measurements. In order to guarantee that the number was measured all the way up to the units place, we need to include the decimal point, even though we are not going to write any decimal place value after it.

13. Definition: Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value . We start counting significant figures at the first non-ze ro digit.

14. Jamboard Activity Make a copy of the document Rename it with your name and class e.g. Significant Figures - Layla Veit - 6C Complete the task Share it with me House points for the first 5 to finish it correctly All instructions above need to be followed

15. Lesson 2 Rounding numbers

16. 1 4 6 3 5 2

17. Look at some examples Round each of these numbers to 1 decimal place (d.p.) 0.46 0.32 12.59 2.362 ≈ 0.5 ≈ 0.3 ≈ 12.6 ≈ 230.1 ≈ 20.3 ≈ 3.0 ≈ 13.0 230.05 20.347 2.98 12.95 ≈ 2.4

18. We round numbers when all we need is a reasonable approximation rather than the exact value . 12.3864 Round the number to 1 d.p. 1st - Identify which digit do we have at the tenths place. 2nd - Draw a line right after this digit. 3rd - Identify which digit comes right after (on the right-hand side) 4th - If the number after the line is less than 5, then round the number down. If the number after the line if greater than or equal to 5, round the number up. ≈ 12. 4

19. We round numbers when all we need is a reasonable approximation rather than the exact value . 3 . 615 Round the number to 2 d.p. 1st - Identify which digit do we have at the hundreadths place. 2nd- Draw a line right after this digit. 3rd - Identify which digit comes right after (on the right-hand side) 4th - If the number after the line is less than 5, then round the number down. If the number after the line if greater than or equal to 5, round the number up. ≈ 3.62

20. We round numbers when all we need is a reasonable approximation rather than the exact value . 73 .95 Round the number to 1 d.p. 1st - Identify which digit do we have at the tenths place. 2nd- Draw a line right after this digit. 3rd - Identify which digit comes right after (on the right-hand side) 4th - If the number after the line is less than 5, then round the number down. If the number after the line if greater than or equal to 5, round the number up. ≈ 74.0

21. We round numbers when all we need is a reasonable approximation rather than the exact value . 126.47 Round the number to the nearest whole number 1st - Identify which digit do we have at the units place. 2nd - Draw a line right after this digit. 3rd - Identify which digit comes right after (on the right-hand side) 4th - If the number after the line is less than 5, then round the number down. If the number after the line if greater than or equal to 5, round the number up. ≈ 126

22. We round numbers when all we need is a reasonable approximation rather than the exact value . 438.5 Round the number to the nearest hundread number 1st - Identify which digit do we have at the hundreads place. 2nd - Draw a line right after this digit. 3rd - Identify which digit comes right after (on the right-hand side) 4th - If the number after the line is less than 5, then round the number down. If the number after the line if greater than or equal to 5, round the number up. ≈ 400

23. Lesson 3 Rounding to significant figures

24. We round numbers when all we need is a reasonable approximation rather than the exact value . 1355.67 Round the number to the nearest ten number 1st - Identify which digit do we have at the ten place. 2nd - Draw a line right after this digit. 3rd - Identify which digit comes right after (on the right-hand side) 4th - If the number after the line is less than 5, then round the number down. If the number after the line if greater than or equal to 5, round the number up. ≈ 1360

25. 3 decimal places 1.566 4 significant figures or Let’s not forget about the significant figures 3 decimal places 1 decimal place 0.057 0.6 2 significant figures or 1 significant figures or

26. Rounding to Significant Figures 2206 1st - Identify 3rd significant figure of the number. 2nd - Draw a line right after this digit. 3rd - Identify which digit comes right after (on the right-hand side) 4th - If the number after the line is less than 5, then round the number down. If the number after the line if greater than or equal to 5, round the number up. ≈ 2210 Round the number to 3 s.f.

27. Rounding to Significant Figures 1.2387 1st - Identify 2nd significant figure of the number. 2nd - Draw a line right after this digit. 3rd - Identify which digit comes right after (on the right-hand side) 4th - If the number after the line is less than 5, then round the number down. If the number after the line if greater than or equal to 5, round the number up. ≈ 1.2 Round the number to 2 s.f.

28. Rounding to Significant Figures .187 1st - Identify 2nd significant figure of the number. 2nd - Draw a line right after this digit. 3rd - Identify which digit comes right after (on the right-hand side) 4th - If the number after the line is less than 5, then round the number down. If the number after the line if greater than or equal to 5, round the number up. ≈ 0.19 Round the number to 2 s.f.

29. Jamboard Activity Make a copy of the document Rename it with your name and class e.g. Rounding - Layla Veit - 6C Complete the task Share it with me House points for the first 5 to finish it correctly All instructions above need to be followed

30. Lesson 4 Estimating results

31. Jhon is at the supermarket and he decides to buy 8 apples, 5 lemons and 3 mangos. Below you can see the price per unit of each of these fruits. Jhon does not have a calculator with him at the time, but he wants to have an idea of how much he is going to spend for all of these fruits. What can he do? R$0.43 R$2.45 R$0.75 8 x R$1.00 = R$8.00 5 x R$0.50 = R$2.50 3 x R$2.00 = R$ R$6.00 R$8.00 + R$2.50 + R$6.00 = R$16.50 We can estimate that Jhon is going to spend R$16.50 on fruits.

32. To estimate a calculation, we can always round all the numbers to 1 significant figure and do the calculation using these numbers. This will give us an idea about the size of the number. → Round all the numbers to 1 s.f. → Don’t forget we should always solve what is inside the brackets first.

33. As we rounded all the numbers down, we have for sure a underestimated value of the real answer. The real answer is 2,682.899. However 2,400 gives us a good idea about the size of the number, Is 2,400 a good estimation?

34. Estimate this value in your notebook. ( 2 + 8 ) x ( 7 + 7 ) = ( 10 ) x ( 14 ) = 140

35. Quick Fire Questions Get ready! Topics Multiple and Factors Index form Square root/numbers Significant figures Rounding Estimating

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46. Quick Fire Questions Poly lives in a small town of 631 people. Every day each person gets one plastic bag from the local shop. If all these people in the town decided to use their own bags instead, roughly how many plastic bags would be saved in a year? 180,000 200,000 240,000 260,000

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