Explore the remainders when powers of 10 are divided by 3. Explain why this method works. Class 8

Explore the remainders when powers of 10 are divided by 3. Explain why this method works. Class 8

Question 1.

Explore the remainders when powers of 10 are divided by 3. Explain why this method works. Class 8

Solution:

When power of 10 are divided by 3, then the remainder in each case is 1 (like by division by 9). Further, for the number like 345, these remainders will be taken as 3 × 1 + 4 × 1 + 5 = 12 (same as in the case of 9), which is divisible by 3. So, 345 is divisible by 3.

Question 2.

Using these observations, can you tell whether the number 462 is divisible by 11? Class 8

Solution:

Yes, 462 is divisible by 11, because 4 + 2 - 6 = 0, which is divisible by 11.