Question

how much longer is a 1-inch button than a 3/8-inch button?

Answer 1

5/8 inches longer since 8/8 - 3/8 = 5/8

Answer 2

we know that

The button has the shape of a circle

the circumference of a circle is equal to

$C=\pi D$

where

D is the diameter of a circle

Step $1$

Find the circumference of the 1-inch button

In this case we have that the diameter is equal to

$D1=1\ in$

substitute the value in the formula

$C1=\pi*1= \pi\ in$

Step $2$

Find the circumference of the 3/8-inch button

In this case we have that the diameter is equal to

$D2=3/8\ in$

substitute the value in the formula

$C2=\pi*3/8= 3\pi/8\ in$

Step $3$

Find the difference of their circumferences

$C1-C2=\pi-3\pi/8=5\pi/8\ in$

therefore

the answer is

$5\pi/8\ in$