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Citation preview
8.0 100
80
50
40
454
343
54
43
54
43
(actual answer = 0.796)
0.5% error
Convert to decimal:
.333...0 3
2
24
16
48
32
96
64
96
64
No approximation.
Answer is exact.
Convert to decimal:
.571428...0 7
5
70
50
35
25
35
25
No approximation.
Answer is exact.
Convert to decimal:
14-28-57-14-28-57....
.960 100
96
50
48
941
939
41
39
41
39
Convert to decimal:
(actual answer = 0.951...)
1% error
.333...0
3
1
133
131
39
13
39
13
Convert to decimal:
No approximation.
Answer is exact.
.333...0
3
1
173
171
51
17
51
17
Convert to decimal:
No approximation.
Answer is exact.
.120 100
12
50
6
25
3
25
3
Convert to decimal:
No approximation.
Answer is exact.
.1250
8
1
38
31
24
3
24
3
Convert to decimal:
No approximation.
Answer is exact.
.111...0
9
1
39
31
27
3
27
3
Convert to decimal:
No approximation.
Answer is exact.
.750 4
3
12
9
120
90
120
90
Convert to decimal:
No approximation.
Answer is exact.
.3750 8
3
16
6
16
6
Convert to decimal:
No approximation.
Answer is exact.
.050 100
5
99
5
99
5
Convert to decimal:
(0.01% error)
Small by about 1%
0.0505 0.0005 .050
.0750 10
1
4
3
40
3
40
3
Convert to decimal:
No approximation.
Answer is exact.
..33.3103
1 10
6
2
6
20620
Calculate or estimate:
No approximation.
Answer is exact.
90109 109
81
9
810
9.0
819.081
Calculate or estimate:
No approximation.
Answer is exact.
.63 10
36
5
18
15
54
150
540
75
27075270
Calculate or estimate:
No approximation.
Answer is exact.
.777...1 9
71
9
16
27
48
270
480
135
240135240
Calculate or estimate:
No approximation.
Answer is exact.
.030 100
3
50
5.1505.1
Calculate or estimate:
No approximation.
Answer is exact.
3010101
101
3
9 10
303
909
303
9090
3.30
909
3.30909
Calculate or estimate:
No approximation.
Answer is exact.
5 100
500
101
500
01.1
501.15
Calculate or estimate:
0.01% error
Too big by about 1%
4.95 0.05 - 5
10 42
420
2.4
422.442
Calculate or estimate:
No approximation.
Answer is exact.
4 9
36
90
36090360
Calculate or estimate:
No approximation.
Answer is exact.
125 4
5100
4
500
4500
Calculate or estimate:
No approximation.
Answer is exact.
..333.1333 ...333.11000 3
41000
3
4000
34000
Calculate or estimate:
No approximation.
Answer is exact.
$3.30 33 3 x 11
30$ %11 of
Calculate or estimate:
No approximation.
Answer is exact.
$10 80 x 8
1
80$ %5.12 of
Calculate or estimate:
No approximation.
Answer is exact.
12$ %12 of
Calculate or estimate:
No approximation.
Answer is exact.
$1.44 144 12 x 12
About one-tenth.Close to $1.20
150$ %15 of
Calculate or estimate:
No approximation.
Answer is exact.
$22.50 225 25 20 x 10 15 x 15
About one-tenth.Close to $15
40$ %90 of
Calculate or estimate:
No approximation.
Answer is exact.
36$ 4-40
One-tenth smaller
2$ %47 of
Calculate or estimate:
No approximation.
Answer is exact.
$0.94 49 2 x 47
About half
2$ %1 of
Calculate or estimate:
No approximation.
Answer is exact.
02.0$
2$ %5.1 of
Calculate or estimate:
No approximation.
Answer is exact.
$0.03 3 2 5.1 x
50$ %51 of
Calculate or estimate:
No approximation.
Answer is exact.
$25.10 512 5 x 15
Expect an answer which is close to $25
200$ %23 of
Calculate or estimate:
No approximation.
Answer is exact.
$46 64 2 x 32
Roughly a quarter of 200
45$ %45 of
Calculate or estimate:
No approximation.
Answer is exact.
$20.25 25 0x504 54 x 54
Roughly half of 50
35 x 35
Multiplication:
No approximation.
Answer is exact.
1225 25 40 x 03 53 x 53
92 x 31
Multiplication:
No approximation.
Answer is exact.
899 1 - 03 92 x 13 22
82 x 32
Multiplication:
No approximation.
Answer is exact.
896 2 - 03 82 x 23 22
52 x 35
Multiplication:
No approximation.
Answer is exact.
875 5 - 03 52 x 53 22
52 x 36
Multiplication:
No approximation.
Answer is exact.
900 100 x 9 4
100 x 63 52 x 63
521 x 888
Multiplication:
No approximation.
Answer is exact.
111,000 1000 x 111 10008
1 x 888 521 x 888
12 x 11
Multiplication:
No approximation.
Answer is exact.
312 1}12{2 12 x 11
114 x 11
Multiplication:
No approximation.
Answer is exact.
5214 1}11}{14{4 114 x 11
.51 x 42
Multiplication:
No approximation.
Answer is exact.
63 1224 .51 x 42
51 x 4.2
Multiplication:
No approximation.
Answer is exact.
63 1224 5.1 x 42 51 x 4.2
99 x 011
Multiplication:
No approximation.
Answer is exact.
99 99 99 x 011
08$ of 5
4
Multiplication:
No approximation.
Answer is exact.
$64 08$ x 10
8 08$ x
5
4
05$ of 25
4
Multiplication:
No approximation.
Answer is exact.
$8 25
50 x 4 05$ x
25
4
03$ of 15
4
Multiplication:
No approximation.
Answer is exact.
$8 15
30 x 4 03$ x
15
4
01$ of 90
45
Multiplication:
No approximation.
Answer is exact.
$5 10$ of half 01$ of 90
45
41$ of 21
2
Multiplication:
No approximation (except for the dollars and cents rounding)
.331$ 3
4
3
2 x 2
21
14 x 2 41 x
21
2
001$ of 99
19
Multiplication:
0.01% error
19.19$ 0.1991 100
011 x 19
99
001 x 19 001 x
99
19
001$ of 69
34
Multiplication:
0.5% error
$49 001 x 100
49 001 x
50
5.24 001 x
69
34
52$ of 35
18
Multiplication:
22.12$107
9
14
180
140
1800
4
100 x
35
18
exact
34
Square roots:
..833.5 6
1 6
36
11 6
36
216
36
346 34
0.05% error
30
Square roots:
5.5 12
6 6
36
31 6
36
616
36
306 30
0.5% error
26
Square roots:
1.5 50
5 5
50
11 5
25
115
25
265 26
0.02% error
18
Square roots:
52.4 16
11 4
16
214
16
184 18
0.02% error
160
Square roots:
13 160 10 x 61 601
3% error
640
Square roots:
3.25 10
13 24
80
133 8 16.3 8 1064 640
0.007% error
[ENOUGH!]
