Calculate 25.8 70.0 Using The Proper Number of Significant Figures

What Are Significant Figures?

Significant figures, also known as significant digits, are the meaningful digits in a number that carry information about its precision. They indicate how accurately a measurement or calculation has been made. For example, in the number 25.8, the digits 2, 5, and 8 are significant, while the decimal point doesn't count as a significant figure.

Significant figures are important because they help maintain consistency in calculations. When you multiply or divide numbers, the result should have the same number of significant figures as the number with the fewest significant figures in the calculation. When you add or subtract numbers, the result should have the same number of decimal places as the number with the fewest decimal places.

How to Determine Significant Figures

Determining the number of significant figures in a number involves following specific rules:

1. Non-zero digits are always significant. For example, 345 has three significant figures.
2. Any zeros between non-zero digits are significant. For example, 1024 has four significant figures.
3. Leading zeros (zeros before the first non-zero digit) are not significant. For example, 0.0045 has two significant figures.
4. Trailing zeros (zeros after the last non-zero digit) in a number without a decimal point may or may not be significant. For example, 1200 could have 2, 3, or 4 significant figures depending on the context.
5. Trailing zeros in a number with a decimal point are significant. For example, 12.00 has four significant figures.

For the numbers 25.8 and 70.0:

• 25.8 has three significant figures (2, 5, and 8).
• 70.0 has three significant figures (7, 0, and 0).

Calculating with Significant Figures

When performing calculations with significant figures, follow these rules:

1. For multiplication and division, the result should have the same number of significant figures as the number with the fewest significant figures in the calculation.
2. For addition and subtraction, the result should have the same number of decimal places as the number with the fewest decimal places.

In this case, since both numbers have three significant figures, the result of any calculation should also have three significant figures.

Example Calculation

Let's calculate the sum of 25.8 and 70.0 using the proper number of significant figures.

The final result is 95.8, which maintains the proper number of significant figures from the original numbers.

Common Mistakes

When working with significant figures, it's easy to make mistakes. Some common errors include:

• Counting leading zeros as significant figures.
• Ignoring trailing zeros in numbers without decimal points.
• Rounding incorrectly when applying the rules for multiplication, division, addition, and subtraction.

To avoid these mistakes, carefully follow the rules for determining significant figures and apply them consistently in your calculations.