Question

You measure the radius of a wheel to be 4.16 cm. If you multiply it by 2 to get the diameter, should you write the result as 8 cm or as 8.32 cm? Justify your answer.

Short answer

The diameter of the wheel is 8.32 cm.

Step-by-step solution

Step 1. Formula for the relation between the radius and diameter of a circle

Given Data:

The radius of the wheel (R) is $4.16\mathrm{cm}$.

The diameter is a line segment that passes through the center of a circle and touches the circumference of the circle with its endpoints.

The formula for the diameter of a wheel is

$D=2R\dots \left(i\right).$

Step 2. Calculating the radius of the wheel

To find the diameter, take the value of radius in equation (i).

Thus, you have

$\begin{array}{c}D=2\times 4.16\\ =8.32\mathrm{cm}.\end{array}$

The calculated value of the diameter is 8.32 cm.

The value of radius 4.16 cm has three significant digits. By the rules of significant digits, the diameter must also have three significant digits.

The value 8 cm has only one significant digit. In comparison, 8.32 cm has three significant digits, equal to those in 4.16 cm. Therefore, 8.32 cm is the more accurate value of the diameter.