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ANEK [815]
3 years ago
11

What is 0.58 repeating as a fraction?

Mathematics
2 answers:
Flura [38]3 years ago
8 0
I.
x = 0.(58)=0.58585858...
 
      x = 0.58585858...
<u>·100        ·100        </u>        (multiply both sides by100)
100x = 58.585858...
100x = 58 + 0.5858558...
100x = 58 + x
 <u>  -x          -x   </u>               (subtract x from both sides)
 99x  =  58
<u>:99        :99  </u>                (divide both sides by 99)
   x  =  \frac{58}{99}


II.
x = 0.5(8)=0.588888... = 0.5+0.088888...

      y = 0.08888...
<u>·10        ·10        </u>        (multiply both sides by10)
 10y =  0.88888...
<u>·10        ·10        </u>        (multiply both sides by10)
100y = 8.88888..
100y = 8 + 0.88888...
100y = 8 + 10y
 <u>-10y     -10y  </u>                   (subtract 10y from both sides)
  90y = 8
 <u>:90      :90   </u>               (divide both sides by 90)
   y = \frac8{90}

x = 0.5 + y

x=\frac12+\frac8{90}=\frac{1\cdot45}{2\cdot45}+\frac8{90}=\frac{45}{90}+\frac8{90}=\frac{53}{90}

bekas [8.4K]3 years ago
7 0

-- If it's only the ' 8 ' that repeats forever,
then that decimal is equivalent to                53/90 .

-- If the ' 58 ' repeats forever, then
the decimal is equivalent to                        58/99 .
 
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