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Rounding off decimal fractions

14.3 Rounding off decimal fractions

Decimal fractions can be rounded in the same way as whole numbers. They can be rounded to the nearest whole number or to one or more figures after the decimal comma. When a number has many decimal digits, we sometimes round off to simplify the number. Rounding off changes the number, but only by a small amount.

The first thing is to work out which of the digits in the number to focus on: we always look at the digit one place further along than we are rounding the number to. For example, if we are rounding off to the hundredths place – which is the second decimal place – then we must look at the value of the third decimal to decide what to do.

  • If the digit that follows the digit to be rounded is \(5\) or bigger, then we round up to the next number. For example: \(\text{13,5}\) rounded to the nearest whole number is \(14\); \(13,526\) rounded to two decimal places is \(\text{13,53}\).
  • If the digit that follows the digit to be rounded is \(4\) or less, then we round down to the previous number. For example: \(\text{13,4}\) rounded to the nearest whole number is \(13\).

  • \(\text{13,5} \approx 14\)
  • \(\text{13,526} \approx \text{13,53}\)
  • \(\text{13,4} \approx 13\)

The symbol \(\approx\) means “approximately equal to”.

Worked Example 14.2: Rounding off

Round off the following number to the nearest hundredth: \(\text{10,225}\).

Locate the place value that needs to be rounded off.

We are rounding to the hundredths place, so it is the second digit after the comma.

Check the next digit to the right and round off.

It is helpful to separate the number into two parts by drawing a line (\(\vert\)) between the second decimal and the third decimal, like this:

\[\text{10,225} \longrightarrow \text{10,22}\vert5\]

If the number following the line is less than \(5\), we should round down; if it is greater than or equal to \(5\), we round up.

In this case, the number after the line is \(5\). The \(5\) tells us to round up, which means from \(\text{10,225}\) to \(\text{10,23}\). (The number gets larger, that is why it is called rounding “up”.)

We write this as: \(\text{10,225} \approx \text{10,23}\).

Worked Example 14.3: Rounding off

Round off the following number to the nearest tenth: \(\text{21,315}\).

Locate the place value that needs to be rounded off.

We are rounding to the tenths place, so it is the first digit after the comma.

Check the next digit to the right and round off.

It is helpful to separate the number into two parts by drawing a line (\(\vert\)) between the first decimal and the second decimal, like this:

\[\text{21,315} \longrightarrow \text{21,3}\vert15\]

If the number following the line is less than \(5\), we should round down; if it is greater than or equal to \(5\), we round up.

In this case, the number after the line is \(1\). The \(1\) tells us to round down, which means from \(\text{21,315}\) to \(\text{21,3}\) (the number gets smaller - that is why it is called rounding “down”.)

We write this as: \(\text{21,315} \approx \text{21,3}\).

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