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givi [52]
3 years ago
10

Express a decimal number ( ie 0.768) - process description please - as a rational number (96/125)?

Mathematics
1 answer:
Stels [109]3 years ago
5 0

The decimal representation of any number is a linear combination of powers of 10. In other words, given a number like 123.456, we can expand it as

1\cdot10^2+2\cdot10^1+3\cdot10^0+4\cdot10^{-1}+5\cdot10^{-2}+6\cdot10^{-3}

10^{-n}=\dfrac1{10^n} for any n, so the above is the same as

100+20+3+\dfrac4{10}+\dfrac5{100}+\dfrac6{1000}=\dfrac{100000+20000+3000+400+50+6}{1000}=\dfrac{123456}{1000}

Similarly, we can write

0.768=\dfrac{768}{1000}

Now it's a question of reducing the fraction as much as possible. We have \mathrm{gcd}(768,1000)=8 so

\dfrac{768}{1000}=\dfrac{96\cdot8}{125\cdot8}=\dfrac{96}{125}

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<u>Symbols</u>

  • π (pi) ≈ 3.14

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

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  2. Parenthesis
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<u>Geometry</u>

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<u>Step 1: Define</u>

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<u>Step 2: Solve for </u><em><u>d</u></em>

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