talk math explain how you can tell without dividing a 3-digit number divided by a 1-digit will have a quotient of 2 or 3 digits.
If the first digit in the 3-digit number is ≥ than the divisor, the quotient will be 3 digits. Otherwise, it quotient will be two digits.
To determine if a 3-digit number divided by a 1-digit number will have a quotient of 2 or 3 digits, you can use the concept of estimation. Here is how you can go about it:
1. Let's assume the 3-digit number is represented by ABC, where A, B, and C are the digits. So, the number can be written as 100A + 10B + C. Similarly, let's assume the 1-digit number is D.
2. To estimate the quotient, divide the hundreds place digit A by the divisor D. If A/D is greater than or equal to 2, then the estimated quotient will have 3 digits. Otherwise, it will have 2 digits.
3. If A/D is equal to 2, we can have a situation where the thousands digit in the quotient could be nonzero. In such cases, the quotient will be a 3-digit number.
4. Additionally, if the remainder is greater than or equal to D/2, then rounding up occurs during division, resulting in an additional digit in the quotient. However, if the remainder is less than D/2, then the quotient remains the same.
By following these steps, you can estimate whether the quotient of a 3-digit number divided by a 1-digit number will have 2 or 3 digits without actually performing the division.