Question

Round off each of the following numbers to the indicated number of significant digits. a. 0.75555 to four digits b. 292.5 to three digits c. 17.005 to four digits d. 432.965 to five digits

Short answer

The rounded numbers are: a) \(0.7556\), b) \(293\), c) \(17.01\), and d) \(432.97\).

Step-by-step solution

a. Rounding 0.75555 to four digits

1. Identify the first four significant digits: Here, we can see that the four significant digits are 0.7555. 2. Check the number to the right of the last significant digit: The digit next to the last significant digit is 5, which is equal to or greater than 5. 3. Round off the last significant digit: Since we determined that the next digit is equal to or greater than 5, we round up the last significant digit. The rounded number is: \(0.7556\).

b. Rounding 292.5 to three digits

1. Identify the first three significant digits: In this case, the three significant digits are 292. 2. Check the number to the right of the last significant digit: The digit next to the last significant digit is 5, which is equal to or greater than 5. 3. Round off the last significant digit: Since we determined that the next digit is equal to or greater than 5, we round up the last significant digit. The rounded number is: \(293\).

c. Rounding 17.005 to four digits

1. Identify the first four significant digits: Here, we can see that the four significant digits are 17.00. 2. Check the number to the right of the last significant digit: The digit next to the last significant digit is 5, which is equal to or greater than 5. 3. Round off the last significant digit: Since we determined that the next digit is equal to or greater than 5, we round up the last significant digit. The rounded number is: \(17.01\).

d. Rounding 432.965 to five digits

1. Identify the first five significant digits: In this case, the five significant digits are 432.96. 2. Check the number to the right of the last significant digit: The digit next to the last significant digit is 5, which is equal to or greater than 5. 3. Round off the last significant digit: Since we determined that the next digit is equal to or greater than 5, we round up the last significant digit. The rounded number is: \(432.97\).