Question

Jenny opened a package of screws quickly and many of them spilled on the floor. She needs to organize the fasteners according to their diameter from least to greatest. Help Jenny determine in what order the fasteners should be organized. Screw A: 4.375 x 10 7square inches Screw B: 1.5 inches Screw C: 1 7/8 inches Screw D: 0.25 inches Screw E: 1.428 x 10 1square inches

Answer 1

Answer: The order is D, B, C, E, A

Explanation:

We need to order from least to greatest the numbers:

A: 4.375x10^7 in^2

B: 1.5 in^2

C: 1 and 7/8 in^2

D: 0.25 in^2

E: 1.428x10^1 in^2

The first thing we need to do is write all the numbers in the same notation, let's use standard notation

A: 4.375x10^7 in^2 = 4.375*10000000 in^2 = 43750000 in^2

B: 1.5 in^2

C: 1 and 7/8 in^2 = ( 1 + 7/8) in^2 = 15/8 in^2 = 1.875 in^2

D: 0.25 in^2

E: 1.428x10^1 in^2 = 1.428*10 in^2 = 14.28 in^2

Now you can see that the order from least to greatest is:

D, B, C, E, A

Answer 2

We have to compare diameters and arrange them in order smallest to greatest

We can see units for option A and B are in square inches so they represents area. So first we will find diameter from area using formula


`A = \pi r^(2)`

so for choice (A) area is given as
`4.375 * 10^(7)`. So plug this in A place in formula and then solve for radius r


`4.375 * 10^(7) = \pi r^(2)`


`(4.375 * 10^(7))/(\pi) = (\pi r^(2))/(\pi)`


`1.393 * 10^(7) } = r^(2)`


`\sqrt{1.393 * 10^(7)} = \sqrt{r^(2)}`

3731.76 = r

So screw A will have

`diameter = 2 * r = 2 * 3731.76 = 7463.52` inches

Similarly for choice (E) area is
`1.428 * 10^(1) = 14.28`
so again plug in formula


`A = \pi r^(2)`


`14.28 = \pi r^(2)`


`(14.28)/(\pi) = (\pi r^(2))/(\pi)`


`4.5477 = r^(2)`


`√(4.5477) = \sqrt{r^(2)}`

2.13201 = r

So screw E will have

`diameter = 2 * r = 2 * 2.13201 = 4.26402` inches

So diameters of all screws are as follows:

Screw A: 7463.52 inches
Screw B: 1.5 inches
Screw C:
`1(7)/(8) = (1* 8+7)/(8) = (15)/(8) = 1.875` inches
Screw D: 0.25 inches
Screw E: 4.26402 inches

Comparing all numbers 7463.52, 1.5, 1.875, 0.25, 4.26402 we can see that smallest number is 0.25, then comes 1.5, then 1.875 and then 4.26402 and then 7463.52

So order from least to greatest will be screw D (0.25), B(1.5), C(1.875), E (4.26402), A (7463.52).

So thats the order D,B,C,E,A and the final answer