Question

Use exponential notation to express the number 385,500 to a. one significant figure. b. two significant figures. c. three significant figures. d. five significant figures.

Short answer

a. \(3\times 10^{5}\) b. \(3.9\times 10^{5}\) c. \(3.86\times 10^{5}\) d. \(3.8550\times 10^{5}\)

Step-by-step solution

Find the appropriate value of 'a' and 'n' for 385,500

To find 'a' and 'n' for the given number, first express 385,500 in decimal form. Write the number as a product of a number between 1 and 10, and a power of 10. We will write 385,500 as \(3.85500\times 10^{5}\). Now that we have written the number in decimal form, we will convert it into exponential notation with the specified significant figures. a. One significant figure

Round to one significant figure

To round 385,500 to one significant figure, we only consider the first digit, which is 3. So, the number is approximately: \(3\times 10^{5}\). b. Two significant figures

Round to two significant figures

To round 385,500 to two significant figures, we need to consider the first two digits, which are 3 and 8. So, the number is approximately: \(3.9\times 10^{5}\). c. Three significant figures

Round to three significant figures

To round 385,500 to three significant figures, we need to consider the first three digits, which are 3, 8, and 5. So, the number is approximately: \(3.86\times 10^{5}\). d. Five significant figures

Round to five significant figures

To round 385,500 to five significant figures, we need to consider the first five digits, which are 3, 8, 5, 5, and 0. So, the number is approximately: \(3.8550\times 10^{5}\).