1. Chapter 3 Notes

2. 3-1 and 3-2 Rounding and Estimating

3. Rounding Decimals Round 4.2683 to the nearest tenth 4.2683 ----> 4.3 Round 4.2683 to the nearest one. 4.2683 ----> 4.0 5 or greater = round up 4 or less = stays the same

4. Rounding to Estimate Estimate to find a reasonable answer. 135.95 15.90 +24.90

5. Rounding to Estimate - Answers Estimate to find a reasonable answer. 135.95 -->140 15.90 --> 20 +24.90 -->+20 275.90 --> 180

6. ESTIMATING QUOTIENTS Compatible numbers - numbers that are easy to divide mentally. First, round the divisor, and then round the dividend to a compatible number. 6 ÷ 3 = 2 quotient Dividend Divisor Example: 38.9 ÷ 1.79 38.9 ≈ 40 1.79 ≈ 2 40 ÷ 2 ≈ 20

7. Rounding using front-end estimation Estimate to find a reasonable answer. $6.04 + $3.45 + $4.43 19.89 + 22.43 + 18.37 350 + 260 + 975

8. Rounding using clustering Estimate to find a reasonable answer. 44.87 + 42.712 + 43.5 21.37 + 22.99 + 22.15

9. Rounding using clustering - Answers Estimate to find a reasonable answer. 44.87 + 42.712 + 43.5 43 + 43 + 43 = about 129 21.37 + 22.99 + 22.15 22 + 22 + 22 = about 66

10. Examples Estimate. Use method of your choice. 1.8.974 + 2.154 2.600 - 209.52 3.44.87 + 42.712 + 43.5 4.$89.90 - $49.29 5.193.7 * 1.78 6.75.45 ÷ 1.48 7.876.66 * 39.64 8.57.1 ÷ 7.2

11. Examples - Answers Estimate. Use method of your choice. 1.8.974 + 2.154 ≈ 11.1 2.600 - 209.52 ≈ 400 3.44.87 + 42.712 + 43.5 ≈ 129 4.$89.90 - $49.29 ≈ $40 5.193.7 * 1.78 ≈ 380 6.75.45 ÷ 12.48 ≈ 6 7.876.66 * 39.64 ≈ 36000 8.57.1 ÷ 7.2 ≈ 8

12. 3-3 Mean, Median, Mode, and Range Measures of central tendency: Mean Median Mode

13. Mean The sum of the numbers divided by how many numbers there are Example: 2,3,4,5,8,8,12 2+3+4+5+8+8+12=42 42/7=6 The mean is 6

14. Median The middle number when the numbers are written in order and have an odd number of values If you have an even number of values, then you have to find the mean of the 2 middle numbers Example: 2,3,4,5,8,8,12 2 3 4 5 8 8 12 5 is the median

15. Mode The number that occurs the most often There can be one mode, more than one mode, or no mode Example: 2,3,4,5,8,8,12 8 is the mode because 8 occurs the most often

16. Range The difference between the greatest number and the least number Example: 2,3,4,5,8,8,12 12-2 = 10 10 is the range

17. Outlier The data value that is much greater or less than any other data values. An outlier can affect the mean of a group of data Example: 9,9,9,10,12,13,31 31 is the outlier

18. Choosing the best measure Mode -- use when the numbers are not numerical Median -- use when an outlier significantly influences the mean Mean -- use when it is not influenced by an outlier

19. Examples Find the mean, median, mode, and range of each group. Find the best measure of central tendency. 1.47 56 57 63 89 44 56 2.3456 560 435 456 3.8 2 4 9 16 4.33 76 86 92 86

20. Examples - Answers 1.47 56 57 63 89 44 56 - 58.9, 56, 56, 45 2.3456 560 435 456 - 1226.8, 508, none, 3021, median, no mode and outlier affects mean too much 3.8 2 4 9 16 - 7.8, 8, none, 14, mean or median 4.33 76 86 92 86 - 74.6, 86, 86, 59 median or mode, outlier affects mean too much

21. 3-4 Using Formulas Formula: an equation that shows a relationship between quantities that are represented by variables. Perimeter: the distance around a figure P = 2l+2w

22. Examples Formula ==> D=RT 1.R = 38.5m/h, T = 12.5h 2.D = 273 mi, T = 9.75 h

23. Examples - Answers Formula ==> D=RT 1. D= 481.25m 2 R = 28 mi/h

24. Formula ==> F=N/4 + 37 N = number of cricket chirps in one minute F = temperature in degrees Fahrenheit 120 chirps/min

25. Formula ==> F=N/4 + 37 N = number of cricket chirps in one minute F = temperature in degrees Fahrenheit 120 chirps/min F = 120/4 + 37 F = 30 + 37 = 67 Answer

26. Formula ==> P=2L+2W 1. L = 16.5mm W = 11.2mm 2. L = 27.3cm W = 16.8cm

27. Formula ==> P=2L+2W 1. L = 16.5mm W = 11.2mm P = 55.4mm 2.L = 27.3 cm W = 16.8 cm P = 88.2 cm Answers

28. Formula ==> F=1.8C+32 1.C = 58 2.C = 72

29. Formula ==> F=1.8C+32 1. C = 58 F = 136.4 2.C = 72 F = 161.6

30. 3-5 and 3-6 Solving Equations with Decimals

31. Subtracting to Solve an Equation N + 4.5 = -9.7 + - 4.5 + -4.5 N = -14.2 Check --> -14.2 + 4.5 = -9.7

32. Adding to Solve an Equation K + - 14.4 = -18.39 + 14.4 +14.4 K = - 3.99 Check --> -3.99 - 14.4 = -18.39

33. Dividing to Solve an Equation 0.9R = -5.4 0.9 0.9 R = -6 Check --> 0.9(-6) = -5.4

34. Multiplying to Solve an Equation M = -12.5 -7.2 (-7.2)M = -12.5(-7.2) -7.2 M = 90

35. Examples 1.A + 10 = 7.9 2.-1.01 = c - 9 3.Y - (-2.6) = 1.6 4.3.02 + d = 2.91 5.9b = -30.6 6.-10.8 = p / -2.5 7.2.45 = -0.7k 8.Y / 3.7 = 240

36. Examples - Answers 1.A + 10 = 7.9 a=-2.1 2.-1.01 = c - 9 c=7.99 3.Y - (-2.6) = 1.6 y=-1 4.3.02 + d = 2.91 d=-.011 5.9b = -30.6 b=-3.4 6.-10.8 = p / -2.5 p=27 7.2.45 = -0.7k k=-3.5 8.Y / 3.7 = 240 y=88

37. 3-7 Using the Metric System Look at page 158 from book! Look at table on p.159 from book.

38. Converting Metric Units Kilo- hect- deka- UNIT deci- centi- milli- Example: 4.35 L = ____mL Move decimal 3 places to right --> 4.35 L = 4,350 mL

39. Examples 1.3.4 cm = _________ mm 2.197.5 cm = ________m 3.7 L = ________mL 4.87 g = ________kg 5.2.8 m = 280 ___ 6.7.84 cm = 78.4 _____ 7.423 m = 0.423 ______ 8.6.5 km = 650,000 ____

40. Examples - Answers 1.3.4 cm = ___34____ mm 2.197.5 cm = __1.975_m 3.7 L = ___7000__mL 4.87 g = __0.087______kg 5.2.8 m = 280 _cm__ 6.7.84 cm = 78.4 __mm___ 7.423 m = 0.423 __km____ 8.6.5 km = 650,000 _cm___