Question

What is the digit at the hundredths place of the number $(225{)}^{40}$?

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

The correct option is C 6

The last three digits of any number are the same as the remainder when we divide the number by 1000.
$\frac{(225{)}^{40}}{1000}=\frac{5^{80}{.9}^{40}}{1000}=\frac{5^{77}{.9}^{40}}{8}$
$9^{40}=(8+1{)}^{40}$ gives remainder 1 when we divide it by 8
$\frac{5^{77}}{8}=\frac{5.(24+1{)}^{38}}{8}$ leaves a remainder 5
So last three digits of $(225{)}^{40}=125\times 5=625$
So the value of ${100}^{th}$ digits is 6.