# Rounding and Significant Figures

```Dŵr y Felin Comprehensive School
Rounding Methodology Booklet
Rounding
To whole numbers
Examples
1. Round 1.4 to the nearest whole number
1
1.5
2
1.4 is clearly closer to 1 than 2,
so it rounds to 1
2
Technically 1.5 is in the middle, but
we always round up 0.5 to the next
whole number in this case 2
1.4
2. Round 1.5 to the nearest whole number
1
1.5
Summary
To round to the place value required look to the number to the right:
4 or less - the number stays the same (round down)
5 or more - the number increases by 1 (round up)
More examples
Round 65293.4 to the nearest:Whole number
(integer)
6 5 2 9 3 . 4 = 65293
Look to the figure to the right.
It is 4 or less so round down
6 5 2 9 3 . 4 = 65290
Look to the figure to the right.
It is 4 or less so round down
Hundred
6 5 2 9 3 . 4 = 65300
Look to the figure to the right.
It is 5 or more so round up
Thousand
6 5 2 9 3 . 4 = 65000
Look to the figure to the right.
It is 4 or less so round down
Ten
Rounding
To Decimal Places
Round 6.99 to 1 decimal place (1dp)
It is easier to see this on a number line.
6.99
6.8
6.9
7.0
7.1
6.99 is now clearly closer to 7.0 than 6.9 so we have to round up to 7.0
Examples
Round 9.86287 to:1 decimal place
9.86287
Look to the figure to the right.
It is 5 or more so round up.
2 decimal places
9.86287
Look to the figure to the right.
It is 4 or less so round down.
3 decimal places
9.86287
Look to the figure to the right.
It is 5 or more so round up.
Rounding
Significant Figures
Significant Figures and Whole Numbers
Remember that significant figures are always counted from the first non-zero digit.
Example
For the number 284.36
284.36
Significant figure -
1st 2nd 3rd 4th 5th
the 2 is the first significant figure
the 8 is the second significant figure
the 4 is the third significant figure
etc.
It is important to remember that rounding a number gives an approximate value for
that number. It is used when the exact value is not needed.
For example, on one day of the London Olympics there were 892,654 spectators at the
events. Most people would not need to know this exact figure and would be happy
with approximate values of about 890,000 or nearly 900,000.
Notice that the approximate values have been “filled-in” with zeroes to keep the same
order of size.
Examples
Round 76452 to:1 significant figure
7 6 4 5 2 = 80,000
Look to the figure to the right.
It is 5 or more so round up.
2 significant figures
7 6 4 5 2 = 76,000
Look to the figure to the right.
It is 4 or less so round down.
3 significant figures
7 6 4 5 2 = 76,500
Look to the figure to the right.
It is 5 or more so round up.
Rounding
Significant Figures and Decimals
Remember that significant figures are always counted from the first non-zero digit.
Example
For the number 0.04637
0.04 6 3 7
Significant figure -
1st 2nd 3rd 4th
the 4 is the first significant figure
the 6 is the second significant figure
the 3 is the third significant figure
etc.
It is important to keep the same number of zeros between the decimal point and the
first significant figure but there is no need to put zeros after the “rounded” digit.
Examples
Round 0.002736 to:1 significant figure
0.002 736 = 0.003
Look to the figure to the right.
It is 5 or more so round up.
2 significant figures
0.0027 36 = 0.0027
Look to the figure to the right.
It is 4 or less so round down.
3 significant figures
0.00273 6 = 0.00274
Look to the figure to the right.
It is 5 or more so round up.
```