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Skillsheet
Rounding whole numbers
The position of a digit in a number shows its value. This is called place value.
For example, in the numeral 21 054 937 the digits have the following values:
Ten
Hundred
Ten
millions
Millions
thousands
thousands
Thousands
Hundreds
Tens
Units
2
1
0
5
4
9
3
7
See Skillsheet: Place value (MAT07NASS10011) for more details.
Large numbers can be rounded when only approximate values are required. Rounded numbers are easier to
work with and to compare. For example, a town’s population of 18 256 may be rounded to 18 300 (to the
nearest hundred) because 18 256 is closer to 18 300 than 18 200.
18 256
18 200
18 300
Example 1
Round 35 714 to the nearest hundred.
Solution
If we are counting by hundreds, then 35 714 is between 35 700 and 35 800. It is closer to 35 700 than to 35 800
so the rounded answer is 35 700.
35 714 & 35 700 (rounded to the nearest hundred). The symbol ‘&’ means ‘approximately equal to’.
A simple rule for rounding to the nearest hundred is to look at the digit in the next place (the tens digit).
l
If the digit is less than 5, then the hundreds digit stays the same (this is called rounding down).
l
If the digit is 5 or more, then add 1 to the hundreds digit (this is called rounding up).
Then insert 0s in the tens and units places.
Example 2
Round each number to the nearest hundred.
a 8470
b 23 819
c 57 962
Solution
a
Counting by hundreds, 8470 is between 8400 and 8500.
In 8470, the hundreds digit is 4 and the tens digit is 7.
7 is more than 5, so round the number in the hundreds place up. Add 1 to the hundreds digit (4 þ 1 ¼ 5)
and fill the rest of the places with 0s.
8470 & 8500 (rounded to the nearest hundred).
© Cengage Learning Australia Pty Ltd 2011
MAT07NASS10013
Number and Algebra: Number and place value
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b
23 819 is between 23 800 and 23 900.
In 23 819, the hundreds digit is 8 and the tens digit is 1.
1 is less than 5, so round down. The hundreds digit, 8, stays the same.
Fill the rest of the places with 0s.
23 819 & 23 800 (rounded to the nearest hundred).
c
57 962 is between 57 900 and 58 000.
In 57 962, the hundreds digit is 9 and the tens digit is 6.
6 is more than 5, so round up. Add 1 to the hundreds digit (9 þ 1 ¼ 10). Since you cannot have 10 as a
hundreds digit, put 0 and add 1 to the thousands digit (7 þ 1 ¼ 8).
Fill the rest of the places with 0s.
57 962 & 58 000 (rounded to the nearest hundred).
Exercise
1 Round each number to the nearest hundred.
a 3148
b 49 028
c 2597
d 4 934 277
e 5693
f 17 360
g 44 215
h 6751
i 108 537
j 247 959
k 39 441
l 2980
A general rule for rounding numbers
Look at the digit in the next place:
l
if the digit is less than 5 (that is 0, 1, 2, 3 or 4), round down
l
if the digit is 5 or more (that is 5, 6, 7, 8 or 9), round up.
Example 3
Round each number to the nearest thousand.
a 245 182
b 1 570 814
c 89 365
Solution
a
In 245182, the thousands digit is 5. The next digit is 1.
1 is less than 5, so round down. The thousands digit, 5, stays the same.
245 182 & 245 000 (rounded to the nearest thousand).
b
In 1 570 814, the thousands digit is 0. The next digit is 8.
8 is more than 5, so round up. Add 1 to the thousands digit (0 þ 1 ¼ 1).
1 570 814 & 1 571 000 (rounded to the nearest thousand).
c
In 89365, the thousands digit is 9. The next digit is 3.
3 is less than 5, so round down. The thousands digit, 9, stays the same.
89 365 & 89 000 (rounded to the nearest thousand).
© Cengage Learning Australia Pty Ltd 2011
MAT07NASS10013
Number and Algebra: Number and place value
www.nelsonnet.com.au
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Exercise
2 Round each number to the nearest thousand.
a 23 538
b 45 370
c 62 941
d 238 604
e 22 367
f 11 758
g 47 929
h 7411
i 109 520
j 2 381 475
k 89 834
l 14 172
Example 4
Round 21 054 937:
a to the nearest ten
b to the nearest ten thousand
c to the nearest million
Solution
a
In 21 054 937, the tens digit is 3. The next digit is 7.
7 is more than 5, so round up. Add 1 to the tens digit (3 þ 1 ¼ 4).
21 054 937 & 21 054 940 (rounded to the nearest ten).
b
In 21 054 937, the ten thousands digit is 5. The next digit is 4.
4 is less than 5, so round down. The ten thousands digit, 5, stays the same.
21 054 937 & 21 050 000 (rounded to the nearest ten thousand).
c
In 21 054 937, the millions digit is 1. The next digit is 0.
0 is less than 5, so round down. The millions digit, 1, stays the same.
21 054 937 & 21 000 000 (rounded to the nearest million).
Exercise
3 Round each number to the nearest ten.
a 45 819
b 2457
c 8314
d 71 262
e 785
f 1439
g 286
h 1699
i 382
j 1744
k 20 155
l 8288
4 Round 64 218 to the nearest:
a thousand
b hundred
c ten
d ten thousand
5 Round 4792 to the nearest:
a thousand
b hundred
c ten
6 Round 1 327 509 to the nearest:
a to the nearest thousand
b ten thousand
d million
e hundred thousand.
c ten
7 Over the holidays, 27 792 people visited a museum. Write this figure correct to the nearest hundred.
8 The extensions on Nina’s house are quoted as costing $17 464. Write this amount correct to the nearest
$100.
© Cengage Learning Australia Pty Ltd 2011
MAT07NASS10013
Number and Algebra: Number and place value
www.nelsonnet.com.au
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9 The crowd at the football grand final was 104 427. Round this figure to the nearest thousand.
10 A factory produces 725 chairs per day. Round this to the nearest hundred.
11 The distance between Sydney and Brisbane is 998 km. Round this distance to the nearest 100 km.
12 The population of Australia is 19 894 517. Round this figure to the nearest 1000.
© Cengage Learning Australia Pty Ltd 2011
MAT07NASS10013
Number and Algebra: Number and place value
www.nelsonnet.com.au
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Answers
1 a 3100
b 49 000
c 2600
d 4 934 300
e 5700
f 17 400
g 44 200
h 6800
i 108 500
j 248 000
k 39 400
l 3000
2 a 24 000
b 45 000
c 63 000
d 239 000
e 22 000
f 12 000
g 48 000
h 7000
i 110 000
j 2 381 000
k 90 000
3 a 45 820
b 2460
c 8310
d 71 260
e 790
f 1440
g 290
h 1700
i 380
j 1740
k 20 160
l 8290
4 a 64 000
b 64 200
c 64 220
d 60 000
5 a 5000
b 4800
c 4790
6 a 1 328 000
b 1 330 000
c 1 327 510
l 14 000
d 1 000 000
e 1 300 000
7 27 800
8 $17 500
9 104 000
10 700
11 1000 km
12 19 895 000
© Cengage Learning Australia Pty Ltd 2011
MAT07NASS10013
Number and Algebra: Number and place value
www.nelsonnet.com.au