A chemist's experimental work involves making measurements.
The result of a
measurement is a
number multiplied by the unit in which the measurement was made.
A measurement of 3.5 kg indicates the mass of the object is 3.5 times the standard mass that is known as a kilogram.
If you are 1.95 m tall, it means that your height is 1.95 times the standard unit of length known as a metre.
Measurements are
made in
units that are
convenient for the size of the measurement.
Your height may have been measured using a metre rule graduated in cm, and in this case would be reported as 195 cm.
For a variety of reasons, it may be convenient to express the measurement in a larger or smaller unit.
The
change in the unit must be accompanied by an opposite change in the
number so that (new number × new unit) equals (old number × old unit).
If the
new unit is larger, the
number associated with that new unit must be
smaller.
If the
new unit is smaller, the
number associated with that new unit must be
larger.
Unit sizes in the SI system are related through multiplication of powers of 10 as shown in the table.
| prefix | symbol | equivalent to
factor × base unit |
| kilo | k | 103 |
| deci | d | 10–1 |
| centi | c | 10–2 |
| milli | m | 10–3 |
| micro | µ | 10–6 |
| nano | n | 10–9 |
| pico | p | 10–12 |
If the unit change requires the
number to be smaller, the power of 10 multiplied must be negative.
number to be larger, the power of 10 multiplied must be positive.
Example 1: Converting the height in cm described above to the height in m.
The new unit is 100 times bigger; therefore the number must be 100 times smaller.
This means that the exponent on the power of 10 multiplied must be negative!
195 cm = 195 × cm = 195 × 10–2 m = 1.95 m
Example 2: Convert 2.05 m to cm.
The new unit is 100 times smaller, therefore the number must be 100 times bigger.
Thus the exponent on the power of 10 multiplied must be positive!
2.05 m = 2.05 × m = 2.05 × 102 cm = 205 cm