Question

Use base $5$ and exponents to represent $2010$.

• A. $2010=3\times 5^4+1\times 5^3+2\times 5^1$
• B. $2010=3\times 5^3+2\times 5^3+2\times 5^1$
• C. $2010=3\times 5^2+1\times 5^3+2\times 5^1$
• D. $2010=3\times 5^5+1\times 5^3+2\times 5^1$

Answer 1

Answer: (A)

$2010=3\times 5^4+1\times 5^3+2\times 5^1$

We know that, $5^1=5,5^2=25,5^3=125,5^4=625,5^5=3125$

Since, $3125>2010$. So, we take upto $5^4$

Now, if we divide $2010$ by $625$ we get quotient as $3$ and remainder as $135$.

$\therefore 2010=3\times 5^4+135$

Now, $135>125=5^3$

If we divide $135$ by $125$ we get quotient as $1$ and remainder as $10$

$\therefore 2010=3\times 5^4+1\times 5^3+10$

Since, $10<5^2$ and $10>5^1$

So, divide $10$ by $5$ we get quotient $=2$ and remainder $=2$.

Thus, $2010=3\times 5^4+1\times 5^3+2\times 5^1$