Question

Order from least to greatest 4/7,5/8,0.7,72%

Answer 1

`\huge\boxed{(4)/(7);\ (5)/(8);\ 0.7;\ 72\%}`

Explanation:

Two ways.

1. Convert to the decimal:

`(4)/(7)=4:7=0.\overline{571428}\\\\(5)/(8)=5:8=0.625\\\\0.7=0.7\\\\72\%=(72)/(100)=0.72`

therefore

`0.\overline{571428}<0.625<0.7<0.72}`

`(4)/(7);\ (5)/(8);\ 0.7;\ 72\%`

2. Convert to the fractions with common denominator.

`(4)/(7);\ (5)/(8)\\\\0.7=(7)/(10)\\\\72\%=(72)/(100)=(18)/(25)`

`LCD=7\cdot8\cdot5\cdot5=1400\\\\(4)/(7)=(4\cdot200)/(7\cdot200)=(800)/(1400)\\\\(5)/(8)=(5\cdot175)/(8\cdot175)=(875)/(1400)\\\\0.7=(7)/(10)=(7\cdot140)/(10\cdot140)=(980)/(1400)\\\\72\%=(72)/(100)=(72\cdot14)/(100\cdot14)=(1008)/(1400)\\\\(800)/(1400)<(875)/(1400)<(980)/(1400)<(1008)/(1400)`

therefore

`(4)/(7);\ (5)/(8);\ 0.7;\ 72\%`