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Rounding to Decimal Places,
Rounding Decimal Numbers


Rounding to decimal places in Math means rounding a decimal number to a specific decimal place.

Now the amount of decimal places a decimal number has, is just the amount of digits that appear to the right of the decimal point.


Below are some examples:

24.57   is to “2” decimal places,     7.634   is to “3” decimal places,

and

64.5291   is to “4” decimal places.




Rounding Up Decimals, Rounding Down:

Whether you end up rounding up decimals or rounding down decimals, depends on the value of the following digit that’s after the decimal place that is to be rounded to.

If the next digit is  4  or less, we round down.

If the next digit is  5  or more, we round up.


Say we wanted to round the following to 1 decimal place.

0.51 , 0.52 , 0.53 , 0.54   get rounded down to   0.5.

0.55 , 0.56 , 0.57 , 0.58 , 0.59   get rounded up to   0.6.





√2 Decimal Form Example


The number  √2  is a number in Math which has what is called an infinite decimal expansion, that continues on and on without an end.


The decimal form of the number  √2  to the first  7  decimal places is:     1.4142135…

Rounded to 5 decimal places this number becomes.     1.41421

The  6th  decimal digit is  3,  so the  13  in the decimal expansion gets rounded down to  10,  however the  0  on the end is usually not written down in a decimal expansion.


If we want to round to  4  decimal places =>     1.4142

The  5th  decimal digit is  1,  so  21  was again rounded down to  20.

Rounded to 3 decimal places:     1.414

Rounded to 2 decimal places:     1.41

Rounded to 1 decimal place:     1.4





Rounding to Decimal Places Examples



(1.1) 

Round   6.62731   to 3 decimal places.

Solution   

The  3rd  digit after the decimal point is  7,  the next digit after  7  is  3,  so we round down to get:     6.627



(1.2) 

Round   47.225   to 2 decimal places.

Solution   

The  2nd  digit after the decimal point is  2,  the next digit after  2  is  5,  so we round up to get:     47.23



(1.3) 

Round   101.9247648   to 4 decimal places.

Solution   

The  4th  digit after the decimal point is  7,  next digit after  7  is  6,  so we round up to get:     101.9248



(1.4) 

Round   0.0305437734   to 6 decimal places.

Solution   

The  6th  digit after the decimal point is  3,  the next digit after  3  is  7,  so we round up to get:     0.030544





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