Question

1. brianna and chloe are dividing 815.75 ÷ 9. brianna says that the first digit of the quotient is in the hundreds place. chloe says it is in the tens place. who is right? how do you know?

Explanation:

Step1: Analyze the dividend's first digit

The dividend is 815.75, and we are dividing by 9. The first digit of the dividend (8) is less than the divisor (9), so we look at the first two digits (81).

Step2: Determine the place value

When dividing 81 by 9, we get 9. Since we are looking at the first two digits (81, which is in the tens and hundreds place? Wait, no. Wait, 8 is in the hundreds place, 1 in the tens, 5 in the ones. But since 8 < 9, we use 81 (tens and hundreds? Wait, 8 is hundreds, 1 is tens, so 81 is 8 tens and 1 ten? Wait, no. 815.75 is 8 hundreds, 1 ten, 5 ones, 7 tenths, 5 hundredths. So when dividing by 9, since 8 (hundreds place) is less than 9, we take the first two digits: 81 (which is 8 tens and 1 ten? Wait, 8 is in the hundreds place, so 800, 1 is in the tens place, 10. Wait, no, 815 is 8 hundreds, 1 ten, 5 ones. So 8 hundreds is 800, which is 80 tens. Wait, maybe a better way: when dividing, the number of digits in the quotient's first digit depends on how many digits of the dividend we need to take to be greater than or equal to the divisor. Since 8 < 9, we take 81 (the first two digits: 8 hundreds and 1 ten, which is 81 tens? Wait, no, 815.75 divided by 9. Let's do the division: 9 into 81 (since 8 < 9, we use 81). 99=81, so 9 goes into 81 nine times. Now, 81 is in the tens and hundreds place? Wait, 8 is in the hundreds place, 1 is in the tens place, so 81 is 8 tens and 1 ten? No, 8 is hundreds (800), 1 is tens (10), so 800 + 10 = 810? Wait, no, 815.75 is 800 + 10 + 5 + 0.7 + 0.05. So when dividing by 9, we start with the leftmost digit. 9 can't go into 8 (hundreds place), so we move to the next digit, making it 81 (tens place? Wait, 8 is hundreds, 1 is tens, so 81 is 8 tens and 1 ten? No, 81 is 810 + 11? No, 8 is in the hundreds place (8100), 1 is in the tens place (110), so 8100 + 110 = 810? Wait, no, 815 is 8100 + 110 + 51. So 815 divided by 9. Let's compute 990 = 810, which is less than 815. So 90 is 9 tens. Wait, so the first digit of the quotient is in the tens place? Wait, no, 990 = 810, so 815 - 810 = 5, so 815/9 = 90 + 5/9 ≈ 90.555..., so the quotient is approximately 90.555..., so the first digit of the quotient (9) is in the tens place. Therefore, Chloe is right.

Answer:

Chloe is right. Because the first digit of the dividend (8) is less than the divisor (9), we use the first two digits (81) to divide by 9. 81 ÷ 9 = 9, and since we used the first two digits (which include the tens place when considering the place value of 81 in the dividend's structure), the first digit of the quotient (9) is in the tens place.