Decimal places describe how many digits are written after the decimal point in a number. Unlike significant figures, decimal places do not indicate the precision of a measurement — they only describe how a number is written.

For example, the following numbers all have two decimal places:

• • 4.00
  • 12.30
  • 0.45

However, these numbers do not necessarily have the same precision, because decimal places depend on the unit used.

Decimal Places Depend on Units

Consider a length measured as:

• • 25.3 mm
  • 2.53 cm
  • 0.00253 km

Each value has differing decimal places, but they represent the same measurement written in different units.
Decimal places change when units change, but the measurement itself does not become more or less precise.

Decimal Places vs Precision

Decimal places tell us where the number stops, and represent how carefully it was measured.

For example:

• • 1.0 cm
  • 1.00 cm
  • 1.000 cm

These have 1, 2, and 3 decimal places respectively. In Physics we assume that the readings are taken from measuring instruments with different precisions. In this case it could be a ruler, digital calipers and digital micrometer screw gauge.

 

Rounding to Decimal Places

Rounding to decimal places is commonly required in calculations.

Rule for rounding:

• Look at the digit immediately after the required decimal place.
• If it is 5 or more, round up.
• If it is less than 5, leave the digit unchanged.

Examples:

• 3.146 rounded to 2 decimal places → 3.15
• 7.432 rounded to 1 decimal place → 7.4
• 0.099 rounded to 2 decimal places → 0.10

In Physics you will not be asked to give an answer to a certain number of decimal places(d.p). You will be expected to only consider significant figures (with the appropriate unit).

Basics