When writing a scientific paper, it is important to use the correct number of significant figures in your data. Significant figures are the digits in a number that are known with certainty, plus one estimated digit. For example, the number 1.23 has three significant figures because the first two digits are known with certainty and the third digit is an estimate.
The number of significant figures in a number is determined by the following rules:
- All nonzero digits are significant.
- Zeros between nonzero digits are significant.
- Leading zeros are not significant.
- Trailing zeros after a decimal point are significant.
For example, the number 1.00 has three significant figures because the first digit is a nonzero digit, the second digit is a zero between nonzero digits, and the third digit is a trailing zero after a decimal point. The number 0.001 has two significant figures because the first digit is a zero, the second digit is a nonzero digit, and the third digit is a trailing zero after a decimal point.
It is important to use the correct number of significant figures in your data because it can affect the accuracy of your calculations. For example, if you are adding two numbers with different numbers of significant figures, the answer should have the same number of significant figures as the number with the fewest significant figures.
Pain Points
- Not knowing how many significant figures to use in your data.
- Making mistakes in calculations because you used the wrong number of significant figures.
- Losing accuracy in your results.
Motivations
- To improve the accuracy of your scientific work.
- To avoid making mistakes in calculations.
- To communicate your results clearly and effectively.
Strategies
- Learn the rules for determining the number of significant figures in a number.
- Practice using the rules to determine the number of significant figures in different numbers.
- Use a calculator that displays the correct number of significant figures.
Common Mistakes to Avoid
- Using too many significant figures in your data.
- Using too few significant figures in your data.
- Mixing significant figures and non-significant figures in your calculations.
Applications
There are many applications for the concept of significant figures in science. Some of these applications include:
- Determining the accuracy of measurements.
- Performing calculations with measured data.
- Communicating scientific results.
Tables
Table 1. Rules for Determining the Number of Significant Figures in a Number
| Rule | Example | Number of Significant Figures |
|---|---|---|
| All nonzero digits are significant. | 1.23 | 3 |
| Zeros between nonzero digits are significant. | 1.00 | 3 |
| Leading zeros are not significant. | 0.001 | 2 |
| Trailing zeros after a decimal point are significant. | 1.200 | 4 |
Table 2. Examples of Numbers with Different Numbers of Significant Figures
| Number | Number of Significant Figures |
|---|---|
| 1.23 | 3 |
| 1.00 | 3 |
| 0.001 | 2 |
| 1.200 | 4 |
| 0.0001 | 1 |
Table 3. Calculations with Different Numbers of Significant Figures
| Calculation | Result | Number of Significant Figures |
|---|---|---|
| 1.23 + 1.00 | 2.23 | 3 |
| 1.23 – 1.00 | 0.23 | 2 |
| 1.23 * 1.00 | 1.23 | 3 |
| 1.23 / 1.00 | 1.23 | 3 |
Table 4. Common Mistakes to Avoid When Using Significant Figures
| Mistake | Example |
|---|---|
| Using too many significant figures in your data. | Reporting a measurement as 1.234 when only the first three digits are significant. |
| Using too few significant figures in your data. | Reporting a measurement as 1 when the first two digits are significant. |
| Mixing significant figures and non-significant figures in your calculations. | Adding a number with three significant figures to a number with two significant figures and reporting the answer with three significant figures. |