Math Lesson 2.1.8 - Rules of Significant Figures

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Welcome to our Math lesson on Rules of Significant Figures, this is the eighth lesson of our suite of math lessons covering the topic of Rounding and Significant Figures, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Rules of Significant Figures

The following rules are applied to find the number of significant figures for a given number:

The zeroes at the end of whole numbers are not counted as significant figures.
For example, 3900 has only two significant figures: 3 and 9. This is because only these two numbers are considered for any possible rounding. In other words, we can round this number only to the nearest thousand or ten-thousand, as the other digits are zero and it is not necessary to do any rounding with them.
The zeroes at the beginning of any decimal number are not counted as significant figures.
For example, the number 0.0036 has only two significant figures (3 and 6) as we can obtain a meaningful rounding only to the nearest hundredth and thousandth, in which the two above non-zero digits are considered. This is not the case of zeroes at the end of a decimal number. These zeroes are all counted, as they determine the precision of a result. In other words, in practice is not the same thing to write 0.040 m and 0.04 m. in the first case, the value is measured with a precision up to 0.001 m (1 mm therefore), while in the second case, the precision of measurement taken is up to 0.01 m (1 cm therefore).
Any zero in-between two non-zero digits (both in whole number as well as in decimals) are always counted as significant figures.
For example, the number 0.0407 has three significant figures (4, 0 and 7). The other two zeroes are at the beginning of a decimal, so they are not counted.

Example 3

How many significant figures do the following numbers have?

403500
3.0040
0.00150

Solution 3

403500 is a whole number. In such numbers, only the zeroes at the end are not counted as significant. Therefore, this number has four significant figures: 4, 0, 3 and 5.
3.0040 is a decimal number. In such numbers, only zeroes at the beginning are not counted. Therefore, this number has five significant figures (all digits are significant).
0.00150 is a decimal number too. However, in this case there are some zeroes at the beginning, which are not counted as significant. Therefore, this number has only three significant figures: 1, 5 and 0.

Finding the Number of Significant Figures by Expressing the Number in Decomposed (Standard) Form

We can identify the number of significant figures by writing the number in the standard form. In such cases, only the part of the number that comes before the powers of ten is considered as significant. Let's consider again the numbers of the previous question to explain this point. We have:

403500 = 4.035 × 10⁵. In this case, the number has four significant figures: 4, 0, 3 and 5, as they come before the powers of ten.
3.0040 = 3.0040 × 10⁰. Nothing changes to the number, so there are five significant figures in it (all digits are significant).
0.00150 = 1.50 × 10^-3. This number has three digits before the powers of ten, so it has three significant figures.

All these results were obtained earlier, when we calculated the number of significant figures of the above number by means of the first method.

More Rounding and Significant Figures Lessons and Learning Resources

Approximations Learning Material
Tutorial ID	Math Tutorial Title	Revision Notes	Revision Questions
2.1	Rounding and Significant Figures
Lesson ID	Math Lesson Title	Lesson	Video Lesson
2.1.1	What is Rounding
2.1.2	Rounding to the Nearest Ten
2.1.3	Rounding to the Nearest Hundred
2.1.4	Rounding to the Nearest Thousand
2.1.5	Explaining Rounding in the Number Axis
2.1.6	Other Types of Rounding
2.1.7	Significant Figures
2.1.8	Rules of Significant Figures
2.1.9	Applications of Significant Figures

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