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# This is the one, I like!

+1
102
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+1148

How many digits are located to the right of the decimal point when $$\frac{3^6}{6^4\cdot625}$$  is expressed as a decimal?

tertre  Mar 20, 2017
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#1
+4155
+3

$$\frac{3^6}{6^4\cdot625}=\frac{729}{1296\cdot625}=\frac{729}{810,000}=0.0009$$

..so 4

hectictar  Mar 20, 2017
#2
+89765
+3

How many digits are located to the right of the decimal point when   is expressed as a decimal?

$$\frac{3^6}{6^4\times 625}\\ =\frac{3^6}{2^4\times 3^4\times 625}\\ =\frac{3^2}{2^4\times 5^4}\\ =\frac{3^2}{10^4}\\ =9*10^{-4}\\ \therefore\\ \text{4 places after the point}$$

Melody  Mar 20, 2017

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