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07 Jun 2015, 09:20
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If \(\frac{3^4}{2^3*5^6}\) is expressed as a terminating decimal, how many nonzero digits will the decimal have?
A. One
B. Two
C. Three
D. Four
E. Six
A. One
B. Two
C. Three
D. Four
E. Six
07 Jun 2015, 09:20
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Official Solution:
If \(\frac{3^4}{2^3*5^6}\) is expressed as a terminating decimal, how many nonzero digits will the decimal have?
A. One
B. Two
C. Three
D. Four
E. Six
To transform the denominator into a base 10 format, which subsequently enables us to convert the fraction into a decimal of the form 0.xxxx, we should multiply the fraction \(\frac{3^4}{2^3*5^6}\) by \(\frac{2^3}{2^3}\):
\(\frac{3^4}{2^3*5^6}*\frac{2^3}{2^3}=\)
\(=\frac{3^4*2^3}{2^6*5^6}=\)
\(=\frac{81*8}{10^6}=\)
\(=\frac{648}{10^6}=\)
\(=0.000648\).
Answer: C
If \(\frac{3^4}{2^3*5^6}\) is expressed as a terminating decimal, how many nonzero digits will the decimal have?
A. One
B. Two
C. Three
D. Four
E. Six
To transform the denominator into a base 10 format, which subsequently enables us to convert the fraction into a decimal of the form 0.xxxx, we should multiply the fraction \(\frac{3^4}{2^3*5^6}\) by \(\frac{2^3}{2^3}\):
\(\frac{3^4}{2^3*5^6}*\frac{2^3}{2^3}=\)
\(=\frac{3^4*2^3}{2^6*5^6}=\)
\(=\frac{81*8}{10^6}=\)
\(=\frac{648}{10^6}=\)
\(=0.000648\).
Answer: C
General Discussion
11 Jan 2016, 13:39
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In order to have a terminating decimal, you need a power of ten on the bottom.
I re-wrote original equation as:
3^4/(10^3)*5^3
(3^4)*(10^-3) / 5^3
.081/125
And then you don't even need to finish the long division to see that there will be three zeros.
I re-wrote original equation as:
3^4/(10^3)*5^3
(3^4)*(10^-3) / 5^3
.081/125
And then you don't even need to finish the long division to see that there will be three zeros.
