Transcript Rounding and Estimating

Chapter 3 Notes
3-1 and 3-2
Rounding and Estimating
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
Rounding to Estimate
Estimate to find a reasonable answer.
135.95
15.90
+24.90
Rounding to Estimate
- Answers
Estimate to find a reasonable answer.
135.95 --> 140
15.90 -->
20
+24.90 --> +20
275.90 --> 180
ESTIMATING QUOTIENTS
Compatible numbers - numbers that are
easy to divide mentally. First, round the
divisor, and then round the dividend to a
compatible number.
Example:
38.9 ÷ 1.79
Dividend
6÷3=2
quotient
38.9 ≈ 40
1.79 ≈ 2
Divisor
40 ÷ 2 ≈ 20
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
Rounding using clustering
Estimate to find a reasonable answer.
44.87 + 42.712 + 43.5
21.37 + 22.99 + 22.15
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
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
Examples - Answers
Estimate. Use method of your choice.
1.
2.
3.
4.
5.
6.
7.
8.
8.974 + 2.154 ≈ 11.1
600 - 209.52 ≈ 400
44.87 + 42.712 + 43.5 ≈ 129
$89.90 - $49.29 ≈ $40
193.7 * 1.78 ≈ 380
75.45 ÷ 12.48 ≈ 6
876.66 * 39.64 ≈ 36000
57.1 ÷ 7.2 ≈ 8
3-3 Mean, Median, Mode, and
Range
Measures of central tendency:
Mean
Median
Mode
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
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
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
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
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
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
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
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
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
Examples
Formula ==> D=RT
1. R = 38.5m/h, T = 12.5h
2. D = 273 mi, T = 9.75 h
Examples - Answers
Formula ==> D=RT
1. D= 481.25m
2 R = 28 mi/h
Formula ==> F=N/4 + 37
N = number of cricket chirps in one
minute
F = temperature in degrees Fahrenheit
120 chirps/min
Answer
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
Formula ==> P=2L+2W
1. L = 16.5mm W = 11.2mm
2. L = 27.3cm
W = 16.8cm
Answers
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
Formula ==>
1. C = 58
2. C = 72
F=1.8C+32
Formula ==>
1. C = 58
F = 136.4
2. C = 72
F = 161.6
F=1.8C+32
3-5 and 3-6
Solving Equations with
Decimals
Subtracting to Solve an
Equation
N + 4.5 = -9.7
+ - 4.5 + -4.5
N
= -14.2
Check --> -14.2 + 4.5 = -9.7
Adding to Solve an Equation
K + - 14.4 = -18.39
+ 14.4 +14.4
K
= - 3.99
Check --> -3.99 - 14.4 = -18.39
Dividing to Solve an Equation
0.9R = -5.4
0.9R = -5.4
0.9
0.9
R = -6
Check --> 0.9(-6) = -5.4
Multiplying to Solve an
Equation
M = -12.5
-7.2
(-7.2)M = -12.5(-7.2)
-7.2
M = 90
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
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
3-7 Using the Metric System
Look at page 158 from book!
Look at table on p.159 from book.
Converting Metric Units
Kilo- hect- deka- UNIT deci- centi- milliExample:
4.35 L = ____mL
Move decimal 3 places to right -->
4.35 L = 4,350 mL
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 ____
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___