Significant figures

Rounding off numbers to a certain degree of accuracy is often necessary in many applications. For example 5,625,000 can be rounded off to one significant figure to make the figure simple or easy to remember. The figure when rounded off would become 6,000,000 because 5,6000,000 is closer to 6000,000. It can also be rounded off to two significant figures resulting in 5,600,000
Below is an example of another very large number. The number starts and ends with a non-zero digit, therefore all the digits are significant. From the right we have first significant number and so on…

Example

Round 0ff to 2 significant figures 8,452,000…

Our second figure from left has been shown below this can either decrease or increase depending on whether the following number is above/equals or below.

Since the following number is a 5 the number 4 before it will increase to a 5, remember we’re treating 4 as the second significant figure so it will become.

We replace all the following figures with zeros because they’re not significant in the level of accuracy we’re trying to archive. Zero figures are not significant.

Identifying significant Figures

Here are a few rules that you should know when working with significant figures.

• All non-zero digits/figures with a number are significant digits, they’re significant for example, 82 has two significant digits (8 and 2) whilst 12345 has five significant digits (1, 2, 3, 4, and 5)
• Leading zeros within a number are not significant; for example 0.00052 has two significant digits 5 and 2
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Rounding off decimal numbers

Decimal numbers can also be rounded off to a certain degree of accuracy for example; 534.56 can be rounded off to 534.6(4.s.f) 4 significant figures.


You have to always remember that leading zeros do not count as significant numbers, for example;

Example

Round off 4.024 to three significant figures.

Our third most significant figure is a 2. So the answer becomes 4.02 (3.s.f)

Example 2

Round off 0.00045308 to 4 significant figures.

5 is our 4th most significant figure. So the answer becomes 0.0004536 (4.s.f)

Remember to leave a note at the end of your answer for the level of accuracy the answer has been rounded off to, for example (4.s.f). This will show the degree of accuracy the answer has been rounded off to.

And that’s how significant figures work.