# Multiplication problem

I was solving the one physical numerical during which i came through a calculation $$1255\times\left(\frac{170.474}1\right)\times\left(\frac{1000}1\right)\times\left(\frac{1}{48.26}\right)^3$$

Answer given by them is :$1.903\times10^3$

But when i calculated value of $(\frac{1}{48.26})^3$ in calculator it came $0.0000000000$.

So i thought that i am wrong because $0$ multiply by anything should be zero.

but then i multiplied the rest of value with $0.0000000000$ the calculator give me the answer$1.903\times10^3$!! Which was correct answer.

Why did calculator showed that answer??

• Perhaps you didn't use a scientific calculator. – Tunk-Fey Jun 1 '14 at 17:40
• @Tunk-Fey i used advance calculator given in computer – Freddy Jun 1 '14 at 17:41
• Google gives $\dfrac{1}{48.26^3}=8.89688644e-6$. So the problem is with the precision used in your calculator. – Jika Jun 1 '14 at 17:44
• In R it shows [1] 8.896886e-06 which means your calculator stores it but not display it. – zhaoyin.usm Jun 1 '14 at 17:44
• Did you really believe that $(1/48.26)^3=0\>$? – Christian Blatter Jun 1 '14 at 18:31

The calculator probably rounded the number at a specific point (that is what my calculator does). I do not like to use decimals, so I will use fractions. $$1255\times 170.474\times 1000\times \left(\frac{1}{48.26}\right)^3$$ $$=1255\times 170.474\times 1000\times \frac{1}{48.26^3}$$ $$=1255\times 170.474\times 1000\times \frac{1}{112398.871976}$$ $$=213944870\times \frac{1}{112398.871976}$$ $$=\frac{213944870}{112398.871976}$$ Plugging this on my calculator gives me $1903.443213$, which is about $1.903\times 10^3$ (technically it is $1.903443213\times 10^3$, but the calculator probably rounded the decimal).
Even if the calculator gave an answer of $0.000000$, do you really believe that $\left(\frac{1}{48.26}\right)^3=0$? It does not make sense. Just use another calculator like Google's calculator, and you should get $8.89688644e-6$, which is $8.89688644\times 10^{-6}$