Topic 1 - Measurements and Uncertainties Orders of Magnitude
Topic 1 - Measurements and Uncertainties Orders of Magnitude
Topic 1 - Measurements and Uncertainties Orders of Magnitude
Orders of magnitude
In physics, we deal with a wide range of magnitudes. We use tiny values such as the mass of
an electron and huge ones such as the mass of the observable universe. To easily
understand the magnitude of these quantities, we need a way to express them in a simple
form. To do this, we simply write them to the nearest power of ten (rounding up or down as
appropriate).
That is, instead of writing a number such as 10000, we write 104 .
Orders of magnitude are used to get an idea of the scale and differences in scale between
values. It is not an accurate representation of a value. For example, if we take 300, it’s order
of magnitude is 102 , which when we calculate it gives 10 x 10 = 100. Although this is three
times less than the actual value, the point of orders of magnitude is to get a sense of the
scale of the number (‘ball park’), in this case we know the number is within the 100’s.
Distances:
Times:
• All non-zero digits are considered significant, such as 16 (2 sig. figures) and 16.34 (4
sig. figures).
• Zeros placed in between two non-zero digits are significant, such as 205 (3 sig.
figures) and 2004 (4 sig. figures).
• Trailing zeros in a number containing a decimal point are significant (such as
6.5400 (5 sig. figures) note that a number 0.00012300 also has 5 sig. figures as the
leading zeros are not significant).
Calculated values should not be stated to a greater accuracy than that of the original data,
nor should measurements be reported to a greater precision than the equipment used to
obtain them supports.
Rounding
When working with significant figures you will often have to round numbers in order to
express them to the appropriate number of significant figures.
For example:
State 2.342 to three significant figures would be written 2.34.
When representing the number 2.342 to three significant figures we rounded it down to
2.34. This means that when we removed the excess digit, it was not high enough to affect
the last digit that we kept.
Whether to round up or down:
If the first digit in the excess which is being cut off is 5 or higher, we increase the last digit
that we are keeping (and the rest of the number if required). If the first digit in the excess
being cut off is lower than 5, we do not change the last digit which we are keeping.