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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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The number of messages Kaitlyn, Tony and Austin sent are 13, 18 and 72 messages respectively.

<h3>How to write and solve equation?</h3>

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103 = x + (x + 5) + 4(x + 5)

103 = x + x + 5 + 4x + 20

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103 - 25 = 6x

78 = 6x

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x = 13

Number of messages each sent:

Number of messages Kaitlyn sent = x

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Number of messages Tony sent = x + 5

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Number of messages Austin sent = 4(x + 5)

= 4(13 + 5)

= 4(18)

= 72 messages

Learn more about equation:

brainly.com/question/2972832

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