Transcript rounding_using_place_value

© T Madas
Sometimes we have to round numbers
What does rounding mean?
Can you think of
some examples?
© T Madas
Rounding to the nearest 10
Round 37 to the nearest 10
30
37
40
The rounded number must have a zero at the end
© T Madas
Rounding to the nearest 10
Round 154 to the nearest 10
150
154
160
The rounded number must have a zero at the end
© T Madas
Rounding to the nearest 10
Round 125 to the nearest 10
120
125
130
When our number lies halfway between “tens”,
we have agreed to round the number up.
© T Madas
Rounding to the nearest 10
Numbers ending in 1, 2, 3 and 4
get rounded down
Numbers ending in 5, 6, 7 , 8 and 9
get rounded up
Examples:
27
30
68
70
94
90
132
130
146
150
565
570
305
310
481
480
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Rounding to the nearest 100
Round 764 to the nearest 100
700
764
800
The rounded number must have 2 zeros at the end
© T Madas
Rounding to the nearest 100
Round 1235 to the nearest 100
1200
1235
1300
The rounded number must have 2 zeros at the end
© T Madas
Rounding to the nearest 100
Round 850 to the nearest 100
800
850
900
When our number lies halfway between “hundreds”,
we have agreed to round the number up.
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Rounding to the nearest 100
Numbers ending in 0s, 10s, 20s, 30s and 40s
get rounded down
Numbers ending in 50s, 60s, 70s , 80s and 90s
get rounded up
Examples:
237
200
1168
1200
874
900
2032
2000
536
500
5750
5800
350
400
40081
40100
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Rounding to the nearest 1000
Round 7761 to the nearest 1000
7000
7761
8000
The rounded number must have 3 zeros at the end
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Rounding to the nearest 1000
Round 8339 to the nearest 1000
8000
8339
9000
The rounded number must have 3 zeros at the end
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Rounding to the nearest 1000
Round 6500 to the nearest 1000
6000
6500
7000
When our number lies halfway between “thousands”,
we have agreed to round the number up.
© T Madas
Rounding to the nearest 1000
Numbers ending in 00s, 100s, 200s, 300s and 400s
get rounded down
Numbers ending in 500s, 600s, 700s , 800s and 900s
get rounded up
Examples:
2837
3000
1868
2000
4874
5000
2499
2000
5376
5000
29780
30000
7500
8000
45681
46000
© T Madas
Practice Rounding
to the nearest…
© T Madas
Round these numbers to the nearest…
…10
…100
…1000
48
50
209
200
3456
3000
87
90
2867
2900
5349
5000
184
180
3467
3500
89231
89000
145
150
1095
1100
37849
38000
1563
1560
1550
1600
32489
32000
3217
3220
45678
45700
49838
50000
2005
2010
61981
62000
71974
72000
…whole number
2.7
3
27.9
28
31.436
31
4.2
4
7.67
8
764.92
765
10.4
10
33.37
33
0.86
1
© T Madas
Round these numbers to the nearest…
…10
…100
…1000
78
80
279
300
76532
77000
67
70
2557
2600
64543
65000
181
180
23107
23100
37859
38000
125
130
16915
16900
90832
91000
1343
1340
1850
1900
98114
98000
3787
3790
49805
49800
89575
90000
1998
2000
61041
61000
70456
70000
…whole number
2.8
3
37.9
38
37.685
38
8.2
8
7.17
7
344.02
344
11.4
11
39.67
40
0.81
1
© T Madas
Quick Test
on Rounding
to the nearest…
© T Madas
Round these numbers to the nearest…
…10
…100
…1000
48
50
209
200
3456
3000
87
90
2867
2900
5349
5000
184
180
3467
3500
89231
89000
145
150
1095
1100
37849
38000
1563
1560
1550
1600
32489
32000
3217
3220
45678
45700
49838
50000
2005
2010
61981
62000
71974
72000
…whole number
2.7
3
27.9
28
31.436
31
4.2
4
7.67
8
764.92
765
10.4
10
33.37
33
0.86
1
© T Madas
Round these numbers to the nearest…
…10
…100
…1000
78
80
279
300
76532
77000
67
70
2557
2600
64543
65000
181
180
23107
23100
37859
38000
125
130
16915
16900
90832
91000
1343
1340
1850
1900
98114
98000
3787
3790
49805
49800
89575
90000
1998
2000
61041
61000
70456
70000
…whole number
2.8
3
37.9
38
37.685
38
8.2
8
7.17
7
344.02
344
11.4
11
39.67
40
0.81
1
© T Madas
© T Madas
Rounding decimals… to the nearest whole number
We look at the 1st decimal place
• If it is 0, 1, 2, 3 or 4 we just throw all the
decimal digits away
• If it is 5, 6, 7, 8 or 9 we throw all the decimal
digits away and we increase the units by 1
Examples:
23.7
24
1.768
2
8.94
9
20.32
20
53.6
54
5.8757
6
3.52
4
40.071
40
© T Madas
Rounding decimals… to one decimal place
We look at the 2nd decimal place
• If it is 0, 1, 2, 3 or 4 we just throw the 2nd, the 3rd,
the 4th … decimal digits away
• If it is 5, 6, 7, 8 or 9 we throw the 2nd, the 3rd, the
4th … decimal digits away and we increase the 1st
decimal digit by 1
Examples:
3.734
3.7
5.728
5.7
8.294
8.3
41.32
41.3
9.16
9.2
5.8757
5.9
6.52
6.5
40.071
40.1
© T Madas
Rounding decimals… to two decimal places
We look at the 3rd decimal place
• If it is 0, 1, 2, 3 or 4 we just throw the 3rd, the 4th,
the 5th … decimal digits away
• If it is 5, 6, 7, 8 or 9 we throw, the 3rd, the 4th, the
5th … decimal digits away and we increase the 2nd
decimal digit by 1
Examples:
3.7342
3.73
5.7028
5.70
5.2863
5.29
4.3592
4.36
0.1605
0.16
5.8957
5.90
2.5782
2.58
4.9971
5.00
© T Madas
Practice Rounding
to Decimal Places
© T Madas
Round the following numbers to 1
2 decimal places
3
3.117
2.724
9.2341
1.9
1.867
1.32
1.3173
2.226
2.2258
5.471
5.5
9.49
9.48973
1.482
1.48173
0.43456
4.1424
0.10704
6.4
6.39745
2.36
2.3553
5.366
5.36581
5.245567
0.47
0.46878
6.401
6.40078
1.6
1.56437
2.59
2.585423
4.090
4.089623
4.7
4.6751
3.5024
3.5004
0.9034
7.31
7.3058
8.533
8.5328
8.8
8.75438
0.50
0.49878
0.500
0.49978
© T Madas
Quick Test
on
Number Rounding
to
Decimal Places
© T Madas
Round the following numbers to decimal places
1 d.p.
2 d.p.
3 d.p.
3.117
2.724
9.2341
1.9
1.867
1.32
1.3173
2.226
2.2258
5.471
5.5
9.49
9.48973
1.482
1.48173
0.43456
4.1424
0.10704
6.4
6.39745
2.36
2.3553
5.366
5.36581
© T Madas
Round the following numbers to decimal places
1 d.p.
2 d.p.
3 d.p.
5.245567
0.47
0.46878
6.401
6.40078
1.6
1.56437
2.59
2.585423
4.090
4.089623
4.7
4.6751
3.5024
3.5004
0.9034
7.31
7.3058
8.533
8.5328
8.8
8.75438
0.50
0.49878
0.500
0.49978
© T Madas
© T Madas