Significant Figures Lesson: Definition, Rules, Rounding and Example

Lesson Overview

• What Are Significant Figures?
• Definition of Significant Figures
• The Importance of Significant Figures
• Rules for Determining Significant Figures
• How to Use Significant Figures in Calculations
• Rounding with Significant Figures

Significant figures are an essential part of math and science, helping us represent numbers accurately. This lesson will teach you the rules and how to use them in different calculations.

What Are Significant Figures?

Significant figures are the important numbers in a value that tell us how precise it is. These numbers include all the digits we know for sure, plus one estimated digit.

Definition of Significant Figures

Significant figures are the digits in a number that are meaningful in terms of accuracy and precision. For example:

• In 2.345, all four digits are significant.

• In 0.00782, only three digits (7, 8, 2) are significant because the leading zeros are not significant.

• In 5040, the digits 5, 0, and 4 are significant, but the last zero is not significant unless specified by a decimal point (e.g., 5040.)

This shows how zeros play a role in determining which digits are significant.

Fig: Significant Figures

The Importance of Significant Figures

Significant figures are important because they show the precision of a measurement or calculation. Scientists and engineers use them to ensure their results are accurate and reliable.

Rules for Determining Significant Figures

1. Non-zero digits are always significant.

• Example: 123 has three significant figures.
  

2. Any zeros between non-zero digits are significant.

• Example: 2003 has four significant figures.
  

3. Leading zeros (zeros before the first non-zero digit) are not significant.

• Example: 0.0045 has two significant figures (4 and 5).
  

4. Zeros to the right of a decimal point and to the right of a non-zero digit are significant.

• Example: 12.340 has five significant figures.
  

5. Trailing zeros in a whole number without a decimal point are not significant.

• Example: 1500 has two significant figures.
  

6. In a measurement value, zeros that occur on the right of the last non-zero digit are significant only if there is a decimal point.

Example: 2650 inches has three significant figures, but if written as 2650. (with a decimal), it has four significant figures.

Here is a table for more clarification.

Number	Significant Figures	Explanation
123	3	All non-zero digits are significant.
2003	4	Zeros between non-zero digits are significant.
0.0045	2	Leading zeros are not significant. Only 4 and 5 are.
12.34	5	Zeros after decimal are significant.
1500	2	Trailing zeros without a decimal are not significant.
1500	5	Decimal makes trailing zeros significant.
0.00782	3	Leading zeros are not significant. 7, 8, and 2 are.
2650	4	Trailing zeros with decimals is significant.

How to Use Significant Figures in Calculations

When performing calculations, it's important to use significant figures correctly to ensure accuracy. The rules for significant figures vary depending on whether you are adding, subtracting, multiplying, or dividing numbers.

Adding Significant Figures

When adding or subtracting numbers, the result should have the same number of decimal places as the number with the fewest decimal places.

Example:

• 12.345 + 1.2 = 13.5 (The result has one decimal place, matching the number with the least decimal places.)

Take This Quiz:

Multiplying Significant Figures

When multiplying significant figures, the result should have the same number of significant figures as the number with the fewest significant figures.

Example:

• 3.45 × 2.1 = 7.2 (The result has 2 significant figures, matching the fewest in the problem.)

Dividing Significant Figures

The same rule applies when dividing: the result should have the same number of significant figures as the number with the fewest significant figures.

Example:

• 45.0 ÷ 6.7 = 6.7 (The result has 2 significant figures, matching the number with the least.)

Take This Quiz:

Rounding with Significant Figures

Rounding with significant figures ensures that the final answer reflects the precision of the original data. Here's how to round numbers correctly:

1. Identify the number of significant figures needed.
   • Determine how many significant figures are required based on the problem or measurement.

2. Round the number accordingly:
   • If the digit after the last significant figure is 5 or more, round up.
   • If the digit after the last significant figure is less than 5, round down.

Examples:

• Round 5.678 to 3 significant figures:
  • Look at the 4th digit (8). Since 8 is greater than 5, round the 7 up to 8. The result is 5.68.

• Round 12.34 to 2 significant figures:
  • Look at the 3rd digit (4). Since 4 is less than 5, leave the 3 unchanged. The result is 12.

• Round 0.004567 to 2 significant figures:

The first two significant digits are 4 and 5. Look at the 3rd digit (6). Since 6 is greater than 5, round the 5 up to 6. The result is 0.0046.

Here is a table to understand it better.

Number	Round to	Rounded Number	Why
5.678	3 significant figures	5.68	Round 7 up because 8 is 5 or more.
12.34	2 significant figures	12	4 is less than 5, so keep 3 as is.
0.004567	2 significant figures	0.0046	Round 5 up because 6 is 5 or more.
9.8765	3 significant figures	9.88	Round 7 up because 6 is 5 or more.
12345	3 significant figures	12300	Round the last two digits to zero.
1500	2 significant figures	1500	Zeros count because they are at the end.

Take This Quiz:

Examples of Significant Figures

1. How many significant figures are in the number 0.00456?

Solution:

There are three significant figures in 0.00456. The leading zeros are not significant, but 4, 5, and 6 are.

2. How many significant figures are in the number 1000?

Solution:

There is only one significant figure in 1000 unless there is a decimal point (e.g., 1000. would have four significant figures). Zeros at the end of a number without a decimal are not significant.

3. Add these numbers applying significant figures rules: 23.45 + 6.7 + 0.093

Solution:

The sum is 30.243.

Since 6.7 has only two significant figures (due to the decimal place), the sum should be rounded to 30.24 (to two decimal places).

4. Add these numbers applying significant figures rules: 23.45 + 6.7 + 0.093

Solution:

The sum is 30.243.

Since 6.7 has only two significant figures (due to the decimal place), the sum should be rounded to 30.24 (to two decimal places).

5. Round 12.378162 to 4 significant figures.

Solution:

When rounding 12.378162 to four significant digits, the number becomes 12.38.

This is because the 8 rounds up the 7 in the thousandth place.

Take This Quiz: