Questions: How many sig figs will the answer to the following problem should be reported with? (657.89+10.0+1.1) × 123.3= 3 significant figures 5 significant figures 4 significant figures 2 significant figures

Solution Steps

First, we need to determine the number of significant figures in each term of the expression:

• \(657.89\) has 5 significant figures.
• \(10.0\) has 3 significant figures.
• \(1.1\) has 2 significant figures.
• \(123.3\) has 4 significant figures.

When adding numbers, the result should be reported with the same number of decimal places as the term with the fewest decimal places.

• \(657.89\) has 2 decimal places.
• \(10.0\) has 1 decimal place.
• \(1.1\) has 1 decimal place.

The term with the fewest decimal places is \(1.1\), which has 1 decimal place. Therefore, the sum \(657.89 + 10.0 + 1.1\) should be reported with 1 decimal place.

When multiplying numbers, the result should be reported with the same number of significant figures as the term with the fewest significant figures.

The sum from Step 2 should be reported with 1 decimal place, which means it will have 4 significant figures (e.g., \(669.0\)).

The number \(123.3\) has 4 significant figures.

Since both numbers involved in the multiplication have 4 significant figures, the result should be reported with 4 significant figures.

Final Answer