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Rounding off a number
 How to simplify a number Rounding to an order of magnitude

Change digits to zeros.

Rounding off a number simplifies it by changing digits to zeros.
You can then crush the zeros by sliding the decimal point using exponential notation.

## To round...

• Decide how many digits you want to keep.
(how many "significant figures").

 Examples... You could round 24314 to 4 significant figures: 24310 to 3 significant figures: 24300 to 2 significant figures: 24000 to 1 significant figure: 20000

If you don't want any at all, see Rounding to an order of magnitude.
(Then you round up from 3 rather than 5).

• Then round away the rest. (round up from 5)

Round up when the first digit being rounded away is 5 or bigger.

Only that single digit matters.
24999 rounded to one place is 20000, not 30000.
The 4 is less than 5, so we don't round up.
The 9's don't matter. They can't make a 4 into a 5.

 Examples... 835049 can be rounded to 835050 (5 significant figures, the 9 rounds up the 83504 to 83505) 835000 (4 significant figures, the 4 doesn't) 835000 (3 significant figures, the 0 doesn't) 840000 (2 significant figures, the 5 rounds up the 83 to 84) 800000 (1 significant figure, the 3 doesn't). 1000000 (No significant figures, order of magnitude).

• You're done.

 A View from the Back of the Envelope Comments encouraged. - Mitchell N Charity