Question

how many sigfigs are in the final answer for (2.5 + 8.6) x 10.0? explain.
calculation:
explanation ( at least one sentence)

Explanation:

Step1: Perform the addition

First, calculate the sum inside the parentheses: \(2.5 + 8.6 = 11.1\)

Step2: Perform the multiplication

Then multiply the result by \(10.0\): \(11.1\times10.0 = 111.0\)

Step3: Determine significant figures

For addition, \(2.5\) (2 sig figs) and \(8.6\) (2 sig figs) give a result with precision to the tenths place, so \(11.1\) (3 sig figs). For multiplication, \(11.1\) (3 sig figs) and \(10.0\) (3 sig figs) result in a number with 3 sig figs (the trailing zero in \(111.0\) is significant here as \(10.0\) has a decimal, but the limiting factor from the addition - multiplication sequence is the 3 sig figs from the addition result's precision and the multiplication factors' sig figs). Wait, actually, when adding \(2.5\) (two decimal places? No, \(2.5\) has one decimal place, \(8.6\) has one decimal place, so the sum should be to one decimal place? Wait, no, \(2.5 + 8.6 = 11.1\) (correct, since \(2.5\) and \(8.6\) have one decimal place, the sum has one decimal place, so \(11.1\) is correct, with three significant figures). Then multiplying by \(10.0\) (three significant figures). When multiplying, the number of significant figures is determined by the least number of significant figures in the factors? Wait, no, for addition, the rule is about decimal places, for multiplication/division, it's about significant figures. So first, addition: \(2.5 + 8.6 = 11.1\) (the result has three significant figures because both \(2.5\) and \(8.6\) have two significant figures? Wait, no, \(2.5\) has two significant figures, \(8.6\) has two significant figures, but when adding, the number of decimal places matters. \(2.5\) has one decimal place, \(8.6\) has one decimal place, so the sum should be reported to one decimal place, which is \(11.1\) (one decimal place, three significant figures). Then multiplication: \(11.1\times10.0\). \(11.1\) has three significant figures, \(10.0\) has three significant figures. So the product should have three significant figures? Wait, \(11.1\times10.0 = 111.0\), but the significant figures: \(11.1\) (3) and \(10.0\) (3), so the result should have 3 significant figures? Wait, no, \(10.0\) is exact? No, \(10.0\) has three significant figures. Wait, maybe I messed up. Let's re - evaluate.

First, addition: \(2.5 + 8.6\). The number of decimal places: \(2.5\) has 1 decimal place, \(8.6\) has 1 decimal place. So the sum is \(11.1\) (1 decimal place), and the number of significant figures in \(11.1\) is 3.

Then multiplication: \(11.1\times10.0\). \(11.1\) has 3 significant figures, \(10.0\) has 3 significant figures. When multiplying, the result should have the same number of significant figures as the factor with the least number of significant figures. Here, both have 3, so the result should have 3 significant figures? Wait, but \(11.1\times10.0 = 111.0\). The trailing zero after the decimal is significant because \(10.0\) has a decimal. But the number of significant figures is determined by the multiplication rule. Wait, maybe the addition step: \(2.5\) (2 sig figs) and \(8.6\) (2 sig figs). When adding, the precision is to the tenths place, so the sum is \(11.1\) (which has 3 sig figs, but the precision is from the decimal places). Then when multiplying by \(10.0\) (3 sig figs), the number of sig figs in the product is determined by the multiplication rule. So \(11.1\) (3 sig figs) \(\times10.0\) (3 sig figs) gives a result with 3 sig figs? Wait, no, \(11.1\times10.0 = 111.0\), which has 4 significant figures? Wait, I think I made a mistake. Let's recall the rules:

1. For addition and subtraction: The result has the same number of decimal places as the term with the least number of decimal places.
- \(2.5\) has 1 decimal place, \(8.6\) has 1 decimal place. So \(2.5 + 8.6=11.1\) (1 decimal place), and the number of significant figures in \(11.1\) is 3.
2. For multiplication and division: The result has the same number of significant figures as the term with the least number of significant figures.
- Now we multiply \(11.1\) (3 significant figures) by \(10.0\) (3 significant figures). So the product should have 3 significant figures? Wait, but \(11.1\times10.0 = 111.0\). Wait, \(10.0\) is a measured value (assuming), so it has 3 significant figures. \(11.1\) has 3 significant figures. So the product should have 3 significant figures. But \(111.0\) has 4? Wait, no, maybe the \(10.0\) is considered as having 3 significant figures, and \(11.1\) has 3. So when we multiply, \(11.1\times10.0 = 111.0\), but we need to round to 3 significant figures? Wait, no, \(11.1\times10.0 = 111.0\), and since both factors have 3 significant figures, the result should have 3 significant figures. But \(111.0\) has 4? Wait, I think the confusion is between decimal places and significant figures. Let's re - express \(10.0\) as \(1.00\times10^{1}\) (3 significant figures) and \(11.1\) as \(1.11\times10^{1}\) (3 significant figures). Multiplying them: \((1.11\times10^{1})\times(1.00\times10^{1})=1.11\times1.00\times10^{2}=1.11\times10^{2}\), which is \(111\) (3 significant figures). Ah, here we go. So the final answer, when expressed in proper significant figure notation, is \(1.11\times10^{2}\), which has 3 significant figures.

Calculation:

1. First, add the numbers inside the parentheses:
- \(2.5+8.6 = 11.1\)
2. Then, multiply the result by \(10.0\):
- \(11.1\times10.0=111.0\). But when considering significant figures, we look at the rules for addition and then multiplication. After addition, we have \(11.1\) (3 significant figures), and when multiplying by \(10.0\) (3 significant figures), the result should have 3 significant figures. So we can write the result as \(1.11\times 10^{2}\) (or \(111\) when considering significant figures, as the trailing zero in \(111.0\) is not significant in terms of the significant figure count from the multiplication rule here? Wait, no, the key is that after addition, we have a number with 3 significant figures, and the multiplier also has 3 significant figures, so the product has 3 significant figures.

Explanation:

First, for the addition \(2.5 + 8.6\), since both numbers have one decimal place, the sum \(11.1\) is reported with one decimal place and has 3 significant figures. Then, when multiplying \(11.1\) (3 significant figures) by \(10.0\) (3 significant figures), the result of a multiplication operation is reported with the same number of significant figures as the factor with the least number of significant figures. Since both factors have 3 significant figures, the final answer has 3 significant figures.

First, for the addition \(2.5 + 8.6\), since both numbers have one decimal place, the sum \(11.1\) is reported with one decimal place and has 3 significant figures. Then, when multiplying \(11.1\) (3 significant figures) by \(10.0\) (3 significant figures), the result of a multiplication operation is reported with the same number of significant figures as the factor with the least number of significant figures. Since both factors have 3 significant figures, the final answer has 3 significant figures.

Answer:

The final answer has 3 significant figures.