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Some of the content of this guide was modeled after a guide originally created by **Openstax**** **and has been adapted for the GPRC Learning Commons in September 2020. This work is licensed under a Creative Commons BY NC SA 4.0 International License.

**General Rules**

**Examples**

- 30525 has
**five**significant figures, four**non-zero digits**, and one**zero between non-zero digits**. - 0.236 has
**three**significant figures, one non-significant**trailing zero**that does not count towards the number of significant figures, and three significant non-zero digits. - 56.00 has four significant figures, two
**non-zero digits**, and two**trailing zeros**to the**left**of the decimal. - 320. has three significant figures because of the
**decimal at the end of this whole number**shows the**trailing zero is significant** - 2500 has two significant figures. Two
**non-zero digits**that are significant and two**non-significant trailing zeros**. Since there is**no decimal at the end**of those trailing zeros they become non-significant. - Numbers that are definitions such as 1 km have
**infinite significant figures.** - 5.02 x 10
^{4 }has**three significant digits**, because of 5.02, 10^{4 }is non-significant based on the above rules. - 55.62 has
**four**significant figures because all the**non-zero numbers**are significant

**Math with Significant Figures**

**Rounding a Number**

When rounding off a number to keep only the amount of significant figures you need use the following rules

- If the number you want to round is followed by 5 or any number greater than five (6,7,8,9) round the number up by one.
- If the number is followed by a number less than five (0,1,2,3,4) then round the number down.

**1 . Addition and Subtraction**

- Count the number of significant digits after the decimal
- Add or subtract the numbers
- The round the final answer to the least number of places in the decimal part of any number

**Example I**

**2.550 + 3.5001 = 6.0501 (We are not done yet!)**

**2.550**has**three**digits after the decimal**3.5001**has**four**digits after the decimal**2.550**has the**least**number of digits after the decimal

Therefore the answer should have **three digits** after the decimal. The fourth number is one. Since it's **less** than five we should round down the final answer to **6.050**

**Example II**

**52.36095 - 32.232 = 20.12895**

**52.36095**has five digits after the decimal**32.232**has three digits after the decimal**32.232**has the least number of digits after the decimal

Therefore the answer should have **three digits** after the decimal. The fourth number is nine. Since it's **greater** than five we should round up the final answer to **20.129**

**2 . Multiplication and Division**

The significant figures in the result, for both multiplication and division, are determined by the least number of significant figures in any number.

**Example I**

An object has a mass of 35.5324 g and a volume of 15.0 cm^{3}, then find the density.

**15.0 cm**^{3 }has the least number of significant figures (**three** significant figures), therefore the answer has **three** significant figures.

- Last Updated: Dec 12, 2021 3:43 PM
- URL: https://libguides.gprc.ab.ca/math
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