# 8.02 Multiplication and Division

## Multiplication and division (implied precision)

The number of significant figures used in the result should be the same as the data with the least number of significant figures. e.g.

2.23 x 102m    x    2.0m     = 4.46 x102 m2     = 4.5 x 102 m2 (rounded up to 2 sig figs)
i.e.     3 sig figs     x    2 sig figs     answer rounded down to 2 sig figs

## Multiplication and division (explicit precision)

When the uncertainty is expressed explicitly then express the uncertainties as percentages and just add them together. e.g.

(10 +/-1mm)     x    (10 +/-1mm)
=(10mm +/- 10% ) m    x    (10mm +/- 10%)
=100mm2 +/- 20% m    = 100 +/- 20mm2

## Multiplication and division by exact values

In most of the section on measurement the term quantity has been used to refer to measureable properties. However it was stated at the outset that the term quantity is also used to simply mean amount. Amounts unlike measurement values can be exact values. e.g. There are exactly four sides on a square, there may be exactly six eggs in a box etc. If a measurement value is multiplied by an exact amount then the uncertainty is also multiplied or divided by this amount. e.g.

(60 +/- 8mm) /4
= 15 +/- 2mm