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Popular Pre Algebra >

Convert to a Simplified Fraction 0.166

  • Pre Algebra
  • Algebra
  • Pre Calculus
  • Calculus
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Solution

tofraction

Solution

50083​
+1
Decimal
0.166
Solution steps
0.166
Multiply and divide by 10 for every number after the decimal point.
There are 3 digits to the right of the decimal point, therefore multiply and divide by 1000
=10000.166⋅1000​
=1000166​
Reduce the fraction 1000166​:50083​
1000166​
Find a common factor of 166 and 1000 in order to cancel it out
Greatest Common Divisor of 166,1000:2
166,1000
Greatest Common Divisor (GCD)
Prime factorization of 166:2⋅83
166
166divides by 2166=83⋅2=2⋅83
2,83 are all prime numbers, therefore no further factorization is possible=2⋅83
Prime factorization of 1000:2⋅2⋅2⋅5⋅5⋅5
1000
1000divides by 21000=500⋅2=2⋅500
500divides by 2500=250⋅2=2⋅2⋅250
250divides by 2250=125⋅2=2⋅2⋅2⋅125
125divides by 5125=25⋅5=2⋅2⋅2⋅5⋅25
25divides by 525=5⋅5=2⋅2⋅2⋅5⋅5⋅5
2,5 are all prime numbers, therefore no further factorization is possible=2⋅2⋅2⋅5⋅5⋅5
The prime factors common to 166,1000 are =2
Factor out 2 from the numerator and the denominator
166=2⋅83,1000=2⋅500
=2⋅5002⋅83​
Cancel the common factor: 2=50083​
=50083​

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Frequently Asked Questions (FAQ)

  • What is tofraction 0.166 ?

    The solution to tofraction 0.166 is 83/500

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