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kodGreya [7K]
3 years ago
7

Please show your work. Convert decimals into fractions in simplest form

Mathematics
1 answer:
Hoochie [10]3 years ago
5 0

Answer:

1. 0.5 = 5/10 ÷ 5 = 1/2

2. 0.7 = 7/10

3. 0.33 = 33/100 ÷ 33 = 1/3

4. 0.875 = (875/1000) ÷ 125 = 7/8

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Bingel [31]

<u>Solution</u><u>:</u>

The rationalisation factor for \frac{1}{ a -  \sqrt{b}  } is a + \sqrt{b}

So, let us apply it here.

\frac{1}{5 -  \sqrt{2} }

The rationalising factor for 5 - √2 is 5 + √2.

Therefore, multiplying and dividing by 5 + √2, we have

=  \frac{1}{5 -  \sqrt{2} }  \times  \frac{5 +  \sqrt{2} }{5 +  \sqrt{2} }  \\  =  \frac{5 +  \sqrt{2} }{(5 -  \sqrt{2})(5 +  \sqrt{2} ) }  \\  =  \frac{5 +  \sqrt{2} }{ {(5)}^{2} - ( \sqrt{2})^{2}   }  \\  =  \frac{5 +  \sqrt{2} }{25 -  2}  \\  =  \frac{5 +  \sqrt{2} }{23}

<u>Answer:</u>

<u>\frac{5 +  \sqrt{2} }{23}</u>

Hope you could understand.

If you have any query, feel free to ask.

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