Question

Indicate the number of significant digits in the answer when each of the following expressions is evaluated (you do not have to evaluate the expression). a. \((6.25) /(74.1143)\) b. (1.45)(0.08431)\(\left(6.022 \times 10^{23}\right)\) c. \((4.75512)(9.74441) /(3.14)\)

Short answer

a. 3 significant digits b. 3 significant digits c. 3 significant digits

Step-by-step solution

a. Determining significant digits in \((6.25) /(74.1143)\)

We are given a division, so the rule for multiplication and division is applied. First, identify the number of significant digits in the terms: 1. \(6.25\) has 3 significant digits. 2. \(74.1143\) has 6 significant digits. The least number of significant digits is 3, so the answer will have 3 significant digits.

b. Determining significant digits in (1.45)(0.08431)\(\left(6.022 \times 10^{23}\right)\)

We are given a multiplication, so the rule for multiplication and division is applied. First, identify the number of significant digits in the terms: 1. \(1.45\) has 3 significant digits. 2. \(0.08431\) has 4 significant digits. 3. \(6.022 \times 10^{23}\) has 4 significant digits. The least number of significant digits is 3, so the answer will have 3 significant digits.

c. Determining significant digits in \((4.75512)(9.74441) /(3.14)\)

We are given a division as well as multiplication, so the rule for multiplication and division is applied. First, identify the number of significant digits in the terms: 1. \(4.75512\) has 6 significant digits. 2. \(9.74441\) has 6 significant digits. 3. \(3.14\) has 3 significant digits. For the multiplication, the least number of significant digits is 6. Now, consider the division. As we found before, the answer from the multiplication will have 6 significant digits. Therefore, we use the numbers of significant digits as: 1. The result of the multiplication (6 significant digits). 2. \(3.14\) having 3 significant digits. The least number of significant digits is 3, so the answer will have 3 significant digits.