Question

Round off each of the following numbers to three significant digits. a. 0.00042557 b. \(4.0235 \times 10^{-5}\) c. 5,991,556 d. 399.85 e. 0.0059998

Short answer

The rounded numbers to three significant digits are: a. 0.000426 b. \(4.02 \times 10^{-5}\) c. 5,990,000 d. 400 e. 0.00600

Step-by-step solution

Identify the first three significant digits

The first three significant digits are 4, 2, and 5.

Determine if the fourth digit rounds up the third digit

The fourth digit is 5, so the third significant digit (5) rounds up to 6.

Write the rounded number

The rounded number is 0.000426. Number b: \(4.0235 \times 10^{-5}\)

Identify the first three significant digits

The first three significant digits are 4, 0, and 2.

Determine if the fourth digit rounds up the third digit

The fourth digit is 3, so the third significant digit (2) remains the same.

Write the rounded number

The rounded number is \(4.02 \times 10^{-5}\). Number c: 5,991,556

Identify the first three significant digits

The first three significant digits are 5, 9, and 9.

Determine if the fourth digit rounds up the third digit

The fourth digit is 1, so the third significant digit (9) remains the same.

Write the rounded number

The rounded number is 5,990,000. Number d: 399.85

Identify the first three significant digits

The first three significant digits are 3, 9, and 9.

Determine if the fourth digit rounds up the third digit

The fourth digit is 8, so the third significant digit (9) rounds up to 10. This causes the second digit (9) to also round up to 10, and the first digit (3) to round up to 4.

Write the rounded number

The rounded number is 400. Number e: 0.0059998

Identify the first three significant digits

The first three significant digits are 5, 9, and 9.

Determine if the fourth digit rounds up the third digit

The fourth digit is 9, so the third significant digit (9) rounds up to 10. This causes the second digit (9) to also round up to 10, making the first digit (5) round up to 6.

Write the rounded number

The rounded number is 0.00600.