Find the estimated quotient for each of the following :
`868 div 38`

Answer

To find the estimated quotient of \( 868 \div 38 \), we will follow these steps:

### Step 1: Round off 868
- The number 868 is a three-digit number. We will round it to the nearest hundred.
- The hundreds place is 8, the tens place is 6, and the units place is 8.
- Since the tens digit (6) is greater than 5, we round up.
- We add 1 to the hundreds place (8 + 1 = 9) and replace the tens and units places with 0.
- Thus, the estimated value of 868 is **900**.

### Step 2: Round off 38
- The number 38 is a two-digit number. We will round it to the nearest ten.
- The tens place is 3 and the units place is 8.
- Since the units digit (8) is greater than 5, we round up.
- We add 1 to the tens place (3 + 1 = 4) and replace the units place with 0.
- Thus, the estimated value of 38 is **40**.

### Step 3: Divide the rounded values
- Now we divide the rounded values: \( 900 \div 40 \).
- We can simplify this division:
- First, we can cancel the common factor of 10 from both numbers:
- \( 900 \div 10 = 90 \) and \( 40 \div 10 = 4 \).
- Now we have \( 90 \div 4 \).

### Step 4: Perform the division
- To divide \( 90 \) by \( 4 \):
- \( 4 \) goes into \( 8 \) two times (since \( 4 \times 2 = 8 \)).
- Subtract \( 8 \) from \( 9 \) to get \( 1 \).
- Bring down the \( 0 \) to make \( 10 \).
- \( 4 \) goes into \( 10 \) two times (since \( 4 \times 2 = 8 \)).
- Subtract \( 8 \) from \( 10 \) to get \( 2 \).
- Now, we can add a decimal point and a zero, making it \( 20 \).
- \( 4 \) goes into \( 20 \) five times (since \( 4 \times 5 = 20 \)).
- Subtract \( 20 \) from \( 20 \) to get \( 0 \).

### Final Result
- Thus, the estimated quotient is **22.5**.
- If we round \( 22.5 \) to the nearest whole number, we get **23**.

### Summary
The estimated quotient of \( 868 \div 38 \) is approximately **23**.