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How to Round Decimal Numbers



Rounding decimal numbers is when we round a decimal number to a certain decimal place.

The amount of decimal places a there are in a decimal number, is the amount of digits that exist on the right side of the decimal point.


Some examples are:

19.38   is to “2” decimal places,     6.735   is to “3” decimal places,

72.6283   is to “4” decimal places.




Rounding Up, Rounding Down

When learning how to round decimal numbers, it;s important to understand about rounding up and rounding down.

Whether or not we round up or round down a decimal number, is something that depends on the value of the following digit that is after the decimal place that we want to round to.

When the next digit is  4  or less, we round down.
When the next digit is  5  or more, we round up.

Consider rounding the following to 1 decimal place.

0.25 , 0.26 , 0.27 , 0.28 , 0.29   get rounded up to   0.30.

0.21 , 0.22 , 0.23 , 0.24   get rounded down to   0.20.




√5 Example

The number  √5  is a number which has an infinite decimal expansion that continues on without an ending place.

The decimal form of  √5  to the first  6  decimal places is:     2.236067…


Round to 4 Decimal Places:

Rounded to  4  decimal places this number will be.     2.2361

The  5th  decimal digit is  6,  which is larger then  5.

So the  0  in the  4th  place of decimal expansion gets rounded up to  1.


Round to 1 Decimal Place:

We can also round to just  1  decimal place, =>     2.2

The  2nd  decimal digit is  3,  which is less than  5.

So  2  is rounded down to  2.0.

Though when learning how to round decimal numbers, we don’t generally write down the  0  for a decimal expansion.





How to Round Decimal Numbers Examples



1.1
Round  4.42825  to  3  decimal places.

Solution

The  3rd  digit after the decimal point is  8,  the next digit after  8  is  2,  so we do a rounding down to get:     4.428



1.2
Round  58.335  to 2 decimal places.

Solution

The  2nd  digit after the decimal point is  3,  the next digit after  3  is  5,  so we do a rounding up to get:     58.34



1.3
Round  204.814673  to 4 decimal places.

Solution

The  4th  digit after the decimal point is  6,  next digit after  6  is  7,  so we perform a rounding up to get:     204.8147



1.4
Round  0.230471883  to 6 decimal places.

Solution

The  6th  digit after the decimal point is  1,  the next digit after  1  is  8,  so we perform a rounding up to get:     0.230472







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