Rounding off

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In mathematics rounding off is writing an answer to a given degree of accuracy.

Let's round off 314 to the nearest hundred.
You know that 314 is closer to 300 than 400, so when we rounded off 314 to the nearest hundred is 300.

Now let's round off 483 to the nearest hundred.
We know that 483 is in between 400 and 500 and it is closer to 500. So, 483 rounded off to the nearest hundred is 500.

This is a another way of looking at it:

In 483, 4 is in Hundreds Place
            8 is in Tens Place
            3 is in Units Place

Hundreds Tens Units or Ones

4 8 3

We want to round off 483 to the nearest hundred.The number to the right of 4 is 8, which is more than 5.So you add 1 to the 4 ie 5 and change the digits in tens and units to zeros

To round off a number correct to a given place,
we round up (that is add 1) if the next figure is 5 or more, we round down (that is just drop them) if the next number is less than 5.

eg: Round off 483 to the nearest hundred.
      8 is more than 5 so we round up to 500.

     Round off 314 to the nearest hundred.
     1 is less than 5, so you just drop14.
     That is we round down to 300.

Examples

(a) Round off 483 to the nearest ten.

Hundreds Tens Units or Ones

4 8 3

In this number 8 represents tens. The number to the right of 8 is 3 which is less than 5, so we round down the number.

(b) Round off 67.32 to the nearest tenth.

Tens Units Tenths Hundredths

6 7 3 2

In this number 3 represents tenths. The number to the right of 3 is 2, which is less than 5, so just leave out 2.

67.32 to the nearest tenth is 67.3

Rounding off to the nearest tenth is sometimes referred to as rounding off to
1 decimal place.

Rounding off to the nearest hundredths is sometimes referred to as rounding off to 2 decimal places.

(d) Round off $ 26.7482 to the nearest cent.

Round off to the nearest cent means round off to the nearest hundredths or round off to two decimal places.

Have a Go

Problem 1

(a) Round off to the nearest ten.
(i) 144

(ii) 1037

(b) Round off to the nearest hundred.
(i) 103

(ii) 1973

(c) Round off to the nearest unit.
(i) 2.8

(ii) 156.39

(d) Round off to the nearest thousand.
(i) 279

(ii) 2908

Problem 2

(a) Round off to the nearest tenth.
(i) 1. 73

(ii) 0.97

(b) Round off to
1 decimal place.
(i) 36.354

(ii) 129.509

(c) Round off to 2 decimal places.
(i) 5.357

(ii) 12.058

(d) Round off to the nearest cent.
(i) $28.7974

(ii) $8.9046

Practice Questions

Question 1
1099, round off to the nearest hundred.

Question 2
853.46, round off to the nearest hundred.

Question 3
2.3, round off to the nearest whole number.

Question 4
17.81, round off to the nearest whole number.

Question 5
6.528, round off to the nearest tenth.(or to 1 decimal place)

Question 6
$23.245, round off to the nearest hundredth.(or to 2 decimal places)

Solutions 1

(a) Round off to the nearest ten.
(i) 144    =140

(ii) 1037 = 1040
4 is less than 5, just drop the
number

3 is in tens,next number which is 7 is more than 5,so just add 1

(b) Round off to the nearest hundred.
(i) 103     = 100

(ii) 1973 = 2000
1 is in hundreds, next number which is0 is less than 5, just drop them.

9 is in hundreds,next number which is 7 is more than 5,so just add 1.

(c) Round off to the nearest unit.
(i) 2.8   = 3
(ii) 156.39 = 156

8 is next to the units which is more than 5, so just add 1. 2+1=3

3 is next to the units which is less than 5, so just drop them.

(d) Round off to the nearest thousand.
(i) 279    = 0
(ii) 2908 = 3000
There is no number in the thousands, 2 is in hundreds which is less than 5, so just drop them.

2 is in thousands, 9 is more than 5 so add 1 to 2 thousand

back to Have a Go

Solutions 2

(a) Round off to the nearest tenth.
(i) 1. 73   = 1.7
(ii) 0.97   = 1.0
7 is in the tenths,the next number3 is less than 5, so just forget them.

9 is in the tenths,the next number7 is more than 5, so add 1.

(b) Round off to
1 decimal place.
(i) 36.354   = 36.4

(ii) 129.509 = 129.5

The number in the second decimal place is5, so add 1,

The number in the second decimal place is 0 which is less than 5, so just drop them

(c) Round off to 2 decimal places.
(i) 5.357   = 5. 36
(ii) 12.058 = 12.06
The number in the third decimal place is7 which is more than 5, so add 1.
The number in the third decimal place is 8 which is more than 5, so add 1.

(d) Round off to the nearest cent.
(i) $28.7974   = $28.80

(ii) $8.9046 = $8.90
When it comes to cents there is only two decimal places, that means we have to round off to 2 decimal places.
7 in the third decimal, which is more than 5, so add 1 to 9
4 is less than 5, so just drop them.

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