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White raven [17]
3 years ago
5

Four plumbers estimated the length of the radius of a cylindrical pipe. The estimates made by the plumbers are listed. Which lis

t shows these lengths in order from greatest to least?

Mathematics
1 answer:
suter [353]3 years ago
6 0

Answer:

\frac{\sqrt{3}}{11}>\frac{\pi }{24}>\frac{3}{25}>\frac{9}{100}

Step-by-step 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.

\frac{3}{25}, \frac{\sqrt{3}}{11}, \frac{9}{100},\frac{\pi }{24}

LCM of the denominators,

2 |<u>  25   11    100   24 </u>

2 |<u>  25    11     50    12 </u>

5 |<u>  25    11     25     6 </u>  

5 |<u>    5     11     5      6  </u>

  <u>     1      11      1       6 </u>

LCM = 2×2×5×5×6×11 = 6600

\frac{3}{25}=\frac{3}{25}\times \frac{264}{264}

   =\frac{792}{6600}

\frac{\sqrt{3}}{11}=\frac{\sqrt{3} }{11}\times \frac{600}{600}

    =\frac{600\sqrt{3}}{6600}=\frac{1039}{6600}

\frac{9}{100}=\frac{9}{100}\times \frac{66}{66}

     =\frac{594}{6600}

\frac{\pi }{24}=\frac{\pi }{24}\times \frac{275}{275}

    =\frac{275\pi }{6600}

    =\frac{864}{6600}

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

\frac{1039}{6600}>\frac{864}{6600}>\frac{792}{6600}>\frac{594}{6600}

\frac{\sqrt{3}}{11}>\frac{\pi }{24}>\frac{3}{25}>\frac{9}{100}

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