Question

Write 0.216 as a rational number in lowest terms

Answer 1

`=(27)/(125)`

Explanation:

`0.216`

`\mathrm{Multiply\:and\:divide\:by\:10\:for\:every\:number\:after\:the\:decimal\:point.}`

`\mathrm{There\:are\:}3\mathrm{\:digits\:to\:the\:right\:of\:the\:decimal\:point,\:therefore\:multiply\:and\:divide\:by\:}1000`

`=(0.216\cdot \:1000)/(1000)`

`=(216)/(1000)`

`216,\:1000`

`\mathrm{The\:GCD\:of\:}a,\:b\mathrm{\:is\:the\:largest\:positive\:number\:that\:divides\:both\:}a\mathrm{\:and\:}b\mathrm{\:without\:a\:remainder}`

`2,\:3\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}`

`=2\cdot \:2\cdot \:2\cdot \:3\cdot \:3\cdot \:3`

`2,\:5\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}`

`=2\cdot \:2\cdot \:2\cdot \:5\cdot \:5\cdot \:5`

`\mathrm{The\:prime\:factors\:common\:to\:}216,\:1000\mathrm{\:are\:}`

`=2\cdot \:2\cdot \:2`

`\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2\cdot \:2=8`

`=8`

`=(8\cdot \:27)/(8\cdot \:125)`

`\mathrm{Cancel\:the\:common\:factor:}\:8`

`=(27)/(125)`

Hence, the correct answer is
`=(27)/(125)`