Question

Four plumbers estimated the length of the radius of a cylindrical pipe. The estimates made by the plumbers are listed. Which list shows these lengths in order from greatest to least?

Answer 1

`(√(3))/(11)>(\pi )/(24)>(3)/(25)>(9)/(100)`

Explanation:

To get the order of the lengths in the order from greatest to least we will make the denominator of the given fractions common and then compare the numerators.

`(3)/(25), (√(3))/(11), (9)/(100),(\pi )/(24)`

LCM of the denominators,

2 | 25 11 100 24

2 | 25 11 50 12

5 | 25 11 25 6

5 | 5 11 5 6

1 11 1 6

LCM = 2×2×5×5×6×11 = 6600

`(3)/(25)=(3)/(25)* (264)/(264)`

`=(792)/(6600)`

`(√(3))/(11)=(√(3) )/(11)* (600)/(600)`

`=(600√(3))/(6600)=(1039)/(6600)`

`(9)/(100)=(9)/(100)* (66)/(66)`

`=(594)/(6600)`

`(\pi )/(24)=(\pi )/(24)* (275)/(275)`

`=(275\pi )/(6600)`

`=(864)/(6600)`

Now we can arrange these fractions in the order of greatest to least.

`(1039)/(6600)>(864)/(6600)>(792)/(6600)>(594)/(6600)`

`(√(3))/(11)>(\pi )/(24)>(3)/(25)>(9)/(100)`