We can round a decimal number to a certain number of decimal places.
To determine whether we round up or round down, we look at the value of the next digit. For example, if we want to round to two decimal places, we look at the value of the third decimal place.

When the value of the next decimal is:

\[\begin{cases}\phantom{x} \lt 5 & \phantom{x} \text{we should round down} \\\phantom{x} \geq5 & \phantom{x} \text{we should round up}\end{cases}\]

Here, rounding down means that the digit we are rounding remains the same. Rounding up means adding #1# to the digit we are rounding. If a digit equals #9#, it becomes a #0#, and the digit in front of it is increased by #1#.

To indicate that a number is rounded and not an exact number, we use the approximation sign (#\approx#) instead of the equal sign (#=#).

Example

#16.184598#

Rounding to

integers: #16#,
because #1 \lt 5#

#1# decimal place: #16.2#,
because #8 \geq 5#

#2# decimal places: #16.18#,
because #4 \lt 5#

#3# decimal places: #16.185#,
because #5 \geq 5#

#4# decimal places: #16.1846#,
because #9 \geq 5#

#5# decimal places: #16.18460#,
because #8 \geq 5#