The smallest number that consists of only 1's and 0's and is exactly divisible by 45 is 1111111110.

Here's how we find it:

1. A number is divisible by 45 if and only if it is divisible by both 5 and 9.

2. For a number to be divisible by 5, its last digit must be 0 or 5. Since the number can only consist of 1's and 0's, the last digit must be 0.

3. For a number to be divisible by 9, the sum of its digits must be a multiple of 9. The smallest such number made up of 1's and 0's is 111111111, which has 9 digits that sum to 9.

4. Therefore, the smallest number that meets both conditions is 1111111110, which is obtained by appending a 0 to the end of 111111111.

5. The number of digits in 1111111110 is 10.

So, the answer is c. 10.

Question

The smallest number that consists of only 1's and 0's and is exactly divisible by 45 is 1111111110.

Here's how we find it:

1. A number is divisible by 45 if and only if it is divisible by both 5 and 9.

2. For a number to be divisible by 5, its last digit must be 0 or 5. Since the number can only consist of 1's and 0's, the last digit must be 0.

3. For a number to be divisible by 9, the sum of its digits must be a multiple of 9. The smallest such number made up of 1's and 0's is 111111111, which has 9 digits that sum to 9.

4. Therefore, the smallest number that meets both conditions is 1111111110, which is obtained by appending a 0 to the end of 111111111.

5. The number of digits in 1111111110 is 10.

So, the answer is c. 10.

Knowee AI · Accepted Answer

The smallest number that consists of only 1's and 0's and is exactly divisible by 45 is 1111111110.

Here's how we find it:

1. A number is divisible by 45 if and only if it is divisible by both 5 and 9.

2. For a number to be divisible by 5, its last digit must be 0 or 5. Since the number can only consist of 1's and 0's, the last digit must be 0.

3. For a number to be divisible by 9, the sum of its digits must be a multiple of 9. The smallest such number made up of 1's and 0's is 111111111, which has 9 digits that sum to 9.

4. Therefore, the smallest number that meets both conditions is 1111111110, which is obtained by appending a 0 to the end of 111111111.

5. The number of digits in 1111111110 is 10.

So, the answer is c. 10.

Find the number of digits in the smallest number consists of only 1's and 0's and exactly divisible by 45?Question 10Answera.900b.45c.10d.0

Question

Solution

Similar Questions

Upgrade your grade with Knowee