What are significant figures?
Significant figures [also known as the significant digits and sig figs for short] are the meaningful digits in a number. They are necessary to indicate the quantity of something. Often, leading zeroes or trailing zeroes can be removed and the number remains just as accurate [005 means the same as 5, for instance].
In order to retain the number’s accuracy, you must be able to identify the significant figures when removing digits. When you round a number up or down, one or some of the sig figs are changed.
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Now let’s get into details
How to calculate significant figures
In order to identify the number of significant figures in a number follow these 3 rules:
- Every digit that is not zero is always significant
- Zeroes found between other digits are significant
- Any trailing zeroes are significant if there is a decimal point
1) Every digit that is not 0 is always significant
2) 0 is significant when it is between other digits, such as 205 or 3.604 [because obviously, 205 is not the same as 25].
3) Any trailing zeroes are significant figures if there is a decimal point [for example 90.7500]. These trailing zeroes might seem unneeded at first glance, but they confirm the precision of the number. 90.75 could be 90.7511 rounded down to two decimal places. Consequently, 90.7500 confirms that it is totally exact to four decimal places.
And these are not significant figures:
1) Leading zeroes before a non-zero digit are not significant figures (00300 is the same as 300, and 008 is the same as 8, so the leading 0s are not significant. They do not make the number any more accurate).
Leading zeros are still not significant figures, even if they come after a decimal point, although this principle can be confusing, it is so. 0.01kg of tomatoes is not the same as 1kg of tomatoes, so the leading zeroes might seem to be significant. However, 0.01kg can also be represented as 10g. It is the same value.
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Thus, leading zeroes are not thought to be significant figures; it is the 1 part that is significant. Certainly, if the zero sits between two significant figures [for example 2.303] then the zero is significant, in line with the rule [2] explained above.
2) Trailing zeroes are not significant when there is no decimal point involved. If there is a decimal point, then, according to rule [3] described above, any trailing zeroes are thought to be significant figures.
Below are some examples of significant figure calculations:
- 8 has 1 significant figure (8).
- 83 has 2 significant figures (8 and 3).
- 200 has 1 significant figure (2).
- 874 has 3 significant figures (8, 7, and 4).
- 458.52 has 5 significant figures (4, 5, 8, 5, and 2).
- 0.0734 has 3 significant figures (7, 3, and 4).
- 40.00 has 4 significant figures (4, 0, 0 and 0) and 2 decimals.
- 0.0035 has 2 significant figures (3 and 5) and 4 decimals.