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