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# Practice Page

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### 102-B: Significant Figures 1: Counting Significant Figures

• Topic Cluster: Science Practice
• Topic: Error Approximation and Significant Figures
• Objective: Given a value in standard or scientific notation, count the number of significant figures in that value.
• Content:
• Level: 1

#### BACK to Ladder Error Approximation and Significant Figures

A significant figure is a digit in a number that you know to be accurate.

#### How to count significant figures:

• Count every digit after the first

For each value, determine how many significant figures there are:

#### An extra rule:

• In a whole number, any zeros at the end of the number are not significant, unless the number ends in a decimal point.

Questions on the extra rule coming soon!

#### The significance of zeroes

Many students wonder why zeroes at the end of the number are considered significant digits. After all, in math class they teach you that 5, 5.0, 5.00, and 5.000 are all the same number. However, in science class, these are NOT the same number! The difference is that, in pure mathematics, numbers are only ideas, theoretical objects whose existence can be deduced from basic axioms. But in science class, numbers represent values that can actually be measured. The number of significant figures, including the zeroes, indicates how accurate that measurement is.

Imagine you are measuring some distance, and find it to be five meters long. Yet, how you write that value is very different.

• If you write "5", you only know that the first digit is 5, and don't know anything about any other digits. The value could be anywhere from 4.5 to 5.4999, because all of these numbers, when rounded, would yield 5.
• If you write "5.0", you know that the tens digit is zero. The value could be anywhere from 4.95 to 5.049999, because all of these numbers, when rounded, would yield 5.0.
• If you write "5.00", you know that the tens and hundreds digits are both zero. The value could be from 4.995 to 5.0049999, because all of these numbers, when rounded, would yield 5.00.
1. Why are some zeroes significant figures?

### Video Resources

##### Flipping Physics Video

This video does not include the rule about adding a decimal point at the end of a number.

#### BACK to Ladder Error Approximation and Significant Figures

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