Rounding decimal numbers 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,
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 0.50.
0.55 , 0.56 , 0.57 , 0.58 , 0.59 get rounded up to 0.60.
√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
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
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
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
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