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Guidance on different ways to round numbers
Rounding and significant places (90 KB , PDF)
Rounding is the process of reducing the number of significant digits in a number. This can help make it easier to remember and use. The result of rounding is a “shorter” number having fewer non-zero digits yet similar in magnitude. The most common uses are where numbers are “longest” – very large numbers rounded to the nearest billion, or million, or very long decimals rounded to one or two decimal places. The result is less precise than the unrounded number.
Example: Turnout in Witney in the 2010 General Election was 73.34%. Rounded to one decimal place (nearest tenth) it is 73.3%, because 73.34 is closer to 73.3 than to 73.4. Rounded to the nearest whole number it becomes 73% and to the nearest ten it becomes 70%. Rounding to a larger unit tends to take the rounded number further away from the unrounded number.
The most common method used for rounding is the following:
Further examples:
For negative numbers the absolute value is rounded.
Examples:
Although it is customary to round the number 4.5 up to 5, in fact 4.5 is no nearer to 5 than it is to 4 (it is 0.5 away from either). When dealing with large sets of data, where trends are important, traditional rounding on average biases the data slightly upwards.
Another method is the round-to-even method (also known as unbiased rounding). With all rounding schemes there are two possible outcomes: increasing the rounding digit by one or leaving it alone. With traditional rounding, if the number has a value less than the half-way mark between the possible outcomes, it is rounded down; if the number has a value exactly half-way or greater than half-way between the possible outcomes, it is rounded up. The round-to-even method is the same except that numbers exactly half-way between the possible outcomes are sometimes rounded up – sometimes down. Over a large set of data the round-to-even rule tends to reduce the total rounding error, with (on average) an equal portion of numbers rounding up as rounding down. This generally reduces the upwards skewing of the result.
The round-to-even method is the following:
Examples:
The process of rounding results in a less precise figure. This explains why rounded percentage totals do not always add up to 100 and why rounded absolute numbers do not always sum to the total.
Rounding to n significant places is a form of rounding by handling numbers of different scales in a uniform way. This gives a rule to where numbers are rounded to. A digit that is closer to the start of a number is “larger” and therefore considered more significant. The number of significant places tell us where to start rounding, from then on the rules are the same.
Examples. Rounding to 2 significant figures:
Rounding to 3 significant figures
Other statistical literacy guides in this series:
Rounding and significant places (90 KB , PDF)
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