Rounding and significant places

This guide is one in a series on different aspects of statistical literacy. The others can be found in the House of Commons Library's Good Information Toolkit.

Rounding is the process of reducing the number of non-zero digits in a number (for example, from 1,593 to 1,600) while keeping a similar magnitude. This can help make it easier to remember and use.

The most common uses are where numbers are very large or very small: large numbers might be rounded to the nearest billion or million, and small numbers might be rounded to one or two decimal places. The result is less precise than the unrounded number, which means, for example, that rounded percentages don’t always add up to 100%.

For example, turnout in Harpenden and Berkhamsted in the 2024 general election was 75.21%. Rounded to one decimal place (the nearest 10th) it is 75.2%. Rounded to the nearest whole number it is 75%, and to the nearest 10 it is 80%.

Rounding to a larger order of magnitude tends to take the rounded number further away from the unrounded number.

Conventional rounding

The most common method used for rounding changes the unrounded number to the closest rounded number:

• Decide what digit to round to (hundreds, thousands, number of decimal places and so on) and therefore how many digits in the number will become zeros.
• If the next digit (the ‘rounding digit’) is 5 or more, increase the first non-zero digit you want to round to by 1 (known as rounding up).
• If the rounding digit is 4 or less, leave the first non-zero digit you want to round to the same (known as rounding down).
• Make the rest of the digits after the one you want to round to 0.

For example:

• 8.074 rounded to two decimal places (hundredths) is 8.07 (because the next digit, 4, is less than 5).
• 8.0747 rounded to two decimal places is 8.07 (the next digit, 4, is less than 5).
• 2,732 rounded to the nearest ten is 2,730 (the next digit, 2, is less than 5)
• 2,732 rounded to the nearest hundred is 2,700 (the next digit, 3, is less than 5)

If a number is negative, we round the same way, as if the minus sign wasn’t there.

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, conventional rounding biases the data slightly upwards, on average.

Round-to-even method (unbiased rounding)

The round-to-even method (also known as unbiased or ‘bankers rounding’) aims to eliminate the tendency of conventional rounding to bias the data upwards. This can be useful when it is important to reduce bias in rounding over larger sets of data where even small biases can reduce accuracy and skew results.

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.

In the round-to-even method, numbers exactly half-way between the possible outcomes are sometimes rounded up, sometimes down, depending on whether the digit is odd or even.

The round-to-even method is the following:

• Decide which digit to round to.
• If the rounding digit is 6 or more, or a 5 followed by one or more non-zero digits, increase the digit you want to round to by 1.
• If the rounding digit is 4 or less, leave the digit you want to round to as it is.
• If the rounding digit is 5 (and the rest of the digits are zeros) and the digit you want to round to is even, leave it as it is. If it’s odd, change it to the nearest even

For example:

• 8.016 rounded to two decimal places is 8.02 (the next digit (6) is 6 or more)
• 8.015 rounded to two decimal places is 8.02 (the next digit is 5, and the previous digit (1) is odd)
• 804,500 rounded to the nearest thousand is 804,000 (the next digit is 5, and the previous digit (4) is even)
• 804,501 rounded to the nearest thousand is 805,000 (the next digit is 5, but it is followed by non-zero digits)

Rounding to a number of significant digits

When numbers are rounded to the same number of significant digits, each of them ends up having the same number of non-zero digits, regardless of how many zeros there are (before the decimal point for large numbers, or after the decimal point for small numbers).

This method can be more useful than rounding to the same order of magnitude (for example, to the nearest hundred) when dealing with numbers of different sizes or a mixture of positive and negative numbers.

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 as for conventional rounding.

For example, when rounding to two significant digits:

• 15,420 becomes 15,000 (the 1 and the 5 are the first two significant figures and the next digit, 4, is less than 5)
• 0.001586 becomes 0.0016
• 0.5 becomes 0.50 (the trailing zero indicates that the number is rounded to 2 significant figures)
• 0.07051 becomes 0.071
• 88,920 becomes 89,000

When rounding to three significant digits:

• 15,420 becomes 15,400 (the 1, 5 and 4 are the first two significant figures and the next digit, 2, is less than 5)
• 0.001586 becomes 0.00159

Rounding to a consistent number of significant digits can be useful in summary financial reporting where the numbers used for income sources, types of costs, profit and so on, can vary considerably and be a mixture of positive and negative numbers. Having a consistent ‘rule’ for rounding to significant digits means all the numbers are rounded to the same degree.

For example, Centrica Group’s 2024 financial statement reported revenue of £19,113 million, gross profit of £4,087 million and post-tax profit of £1,365 million. when rounding to two significant digits these become:

• Revenue of £19,000 million
• Gross profit of £4,100 million
• Post-tax profit of £1,400 million