How do I multiply using sig figs?
To multiply using significant figures (sig figs), you need to follow a few rules. Here's a step-by-step guide:
1. Determine the number of significant figures in each of the factors (the numbers being multiplied).
2. Multiply the factors as you normally would, without considering significant figures.
3. Count the total number of significant figures in the original factors. This will be the number of significant figures in your final product.
4. Round the result to the correct number of significant figures by considering the least precise measurement among the original factors.
Let's walk through an example to illustrate the process:
Suppose you want to multiply 2.35 (with three significant figures) by 1.8 (with two significant figures).
Step 1: Determine the number of significant figures in the factors:
- 2.35 has three significant figures.
- 1.8 has two significant figures.
Step 2: Multiply the factors:
- 2.35 × 1.8 = 4.23 (without considering significant figures).
Step 3: Count the total number of significant figures in the original factors:
- The original factors have three and two significant figures, respectively. Thus, the final result should also have two significant figures.
Step 4: Round the result to the correct number of significant figures:
- Since the least precise measurement has two significant figures (1.8), the final result should also be rounded to two significant figures.
- Therefore, 4.23 would be rounded to 4.2.
Remember to always use the correct number of significant figures in your final answer to maintain accuracy in scientific calculations.