Rounding, S.F and Estimation

Rounding

Rounding is simple.
How you do it depends on what you’re rounding to – eg. the nearest whole, 5 , 10, 100.

When rounding to the nearest ten, you round up when the unit digit is five or over and down when it is not.
Eg: 15 rounds to 20, 13 rounds to 10.
Any other number, such as the nearest five, four, hundred or whatever works much the same way. However, as you get to hundreds, the tens digit is counts, as you get to thousands the hundred digit is what counts and so on.
The nearest five to 27 is 25.
The nearest four to 27 is 28.
The nearest hundred to 489 is 500.
The nearest hundred to 349 is 300.

Rounding to the nearest whole digit is exactly the same, but it uses the values of decimal places.
Eg: 4.3 rounds to 4
4.5 rounds to 5
π   rounds to 3

Significant figures

Significant figures are different.
To round to a number of significant figures, as you may be asked to do, you have to first understand which digits are considered ‘significant’. It is simply all the digits after the first non-zero digit. To round it off, you cut off the number after the number of s.fs you’ve been told to round to. However, you are not just cropping; you must always keep the same number of digits before the number’s decimal point, filling the extras in with zeros when necessary, and some of the prior rounding rules do apply – if the digit after the last s.f is five or over, you add one to the last s.f. If not, you don’t.
Eg:
1295463.009 to 2 s.fs is:
1300000
0.000005619 to 2 s.fs is:
0.0000056

Estimation

Estimation is using rounding and significant figures to easily work out rough estimates for mathematical problems.
Eg:
Estimating (40.35 ÷ 1.91262) x 3.142 in this way only requires you to round each number therein (either way), making (40 ÷ 2) x 3 , which we can easily calculate as 60.
The actual answer is 66.2858801016, we weren’t that far off.

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