VCE Chemistry:
- all digits in numbers expressed in standard form are significant: for example, 4.320 x 10-6 has four significant figures
- all non-zero numbers are significant: for example, 42.3 has three significant figures
- zeros between two non-zero numbers are significant: for example, 4.302 has four significant figures
- leading zeros are not significant: for example, 0.0043 has two significant figures
- trailing zeros to the right of a decimal point are significant: for example, 42.00 has four significant figures
- for numbers less than one, 0.4 has one significant figure and 0.04 also has one significant figure, whereas 0.40 has two significant figures and 0.400 has three significant figures
- whole numbers written without a decimal point will have the same number of significant figures as the number of digits, with the assumption that the decimal point occurs at the end of the number: for example, 400 has three significant figures. Therefore, a stated volume of ‘400 mL’ will be considered as having three significant figures.
Significant Figures is a way to express the confidence we have in our
measurements. In this way we let the number of digits in the measurement
indicate the certainty of the measurement.
For example, the temperature
in an oven is measured at 131.23 oC. We know, with certainty,
all the numbers except the last one, which is an estimate.
Using a stopwatch to measure the time taken for me to run 100m I would
get a measurement of 9.0 seconds. The precision of this stopwatch is such
that my time can be 8.5 or 9.5 seconds. It is fine to say that my time
was about 9 seconds but it is not right to say my time was 8.995 seconds.
It is fine to drop off numbers but we can not just make up numbers as
we wish.
Significant figures are used
in scientific calculations in interpreting measured results and are the
easiest way of indicating the uncertainty in measurements.
Same basic
rules for determining significant numbers follow.
How do we work out how many
significant figures are in a measurement? This is not as clear as it sounds.
The number of significant figures
is the number of digits from the most significant to the least significant
digit.
- The most significant digit
is the left most digit which is not a zero.
- If the number does not have a decimal point the right most digit which
is not a zero is the least significant. If the number does have a decimal
point it is the right most digit, even if the digit is a zero.