Week 13 Rounding & Estimation MATHS Week 13 Rounding & Estimation

Starter! Each table has the ‘starting 6’ worksheet on – can your table answer all 6 questions?

What did we do last week?

Before we begin……

Have you done your directed study? I hope you revised!

What are we going to do this week? Rounding and Estimating Upper and Lower Bounds Truncation Assessment

Rounding and estimating

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 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

Rounding – to the nearest 1000 6 4 8 3 2 1 4 8 3 7 1 0 6 9 5 5 or more? 5 or more? 5 or more? No Yes Yes 6 4 8 0 0 0 5 0 0 0 1 1 0 0 0

Rounding to 1 Decimal Place (1DP) 4 . 8 3 2 5 9 . 3 4 2 5 4 . 8 5 2 5 or more? 5 or more? 5 or more? No No Yes 4 . 8 9 . 3 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 2 Decimal Places: 2DP 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 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

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) 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 Figures (2SF) 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 Figures (3SF) 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 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

The following number could be the population of a country at a particular instant in time.Write this number to 1, 2, 3, 4, 5, 6 and 7 significant figures. 56 345 678 60 000 000 56 000 000 56 300 000 56 350 000 56 346 000 56 345 700 56 345 680

Estimation and Rounding What is… 53 + 26 = 79 50 30 + = 80

67 + 112 = 179 70 110 + = 180

45 + 233 = 278 50 230 + = 280

Exam question using rounding

Upper & Lower Bounds

What are they?

Limits of accuracy https://corbettmaths.com/2013/05/28/lower-and-upper-bounds/

So to find the bounds…… Upper bound = Add on half of whatever it is rounded to Lower bound = Subtract half of whatever it is rounded to

For example The measurement has been rounded to the nearest metre so I need to find half of this. 1m ÷ 2 = 0.5m This is the amount I will add and subtract to find the bounds (limits) UPPER BOUND = 22m + 0.5m = 22.5m LOWER BOUND = 22m – 0.5m = 21.5m

Your turn What is it measured to? Find half of this. Add this on to find the upper bound Take this away to find the lower bound

Exam Question A small van can take a load of up to 1500 kg. This van has to take the following to a market: 50 large bags of potatoes, each bag weighing 25kg to the nearest kg, 240 boxes of oranges, each box weighing 3000 g to the nearest 10 g. Could this load be over the limit? You must show all your working.

Truncation

Truncation Truncation is a way to approximate a number without rounding You always round down at the given unit If someone asks ‘how old are you?’ what do you say?

Truncation

Truncation Mini Whiteboards Truncate 423.28135 To 4 d.p. 423.2813

Truncation Mini Whiteboards Truncate 3123.21 To 1 d.p. 3123.2

Truncation Mini Whiteboards Truncate 123.601 To the whole number 123

Truncation Mini Whiteboards Truncate 23941.412 To the hundreds 23900

If 5.4 has been truncated to 1 d.p. Upper and Lower Bounds How could we describe the Error Interval of a truncated number? If 5.4 has been truncated to 1 d.p. what are the values it could have been? 5.3 5.4 5.5 The Error Interval 5.4 ≤ x < 5.5 5.4 5.5

Find the error interval of 8.2345 truncated to 4 d.p. Upper and Lower Bounds Find the error interval of 8.2345 truncated to 4 d.p. what are the values it could have been? 8.2344 8.2345 8.2346 The Error Interval 8.2345 ≤ x < 8.2346 8.2345 8.2346

What is the Error Interval of Truncation Mini Whiteboards What is the Error Interval of 24.13 Truncated to 2 d.p. 24.13 ≤ x < 24.14

What is the Error Interval of Truncation Mini Whiteboards What is the Error Interval of 14.745 Truncated to 3 d.p. 14.745 ≤ x < 14.746

741 What is the Error Interval of Truncated to a whole number Truncation Mini Whiteboards What is the Error Interval of 741 Truncated to a whole number 741 ≤ x < 742

What is the Error Interval of Truncation Mini Whiteboards What is the Error Interval of 7480 Truncated to the tens 7480 ≤ x < 7490

Round or Truncate?

2nd lesson Half Term Mini Assessment You now have one and a half hours to complete the mini assessment. You are expected to stay for the full time. If you finish the assessment early, use the time wisely to check through your answers.

Directed Study

Your targets… Make sure you have worked on your targets as it is time to review them over the next couple of weeks (hint: if you can’t remember them look on pro-portal)!!!