Question

continue dividing on the algorithm. what is 60 hundredths divided by 8 ones? 0.3 8 longdiv 3.00 -2.4 .60 - .

Explanation:

Step1: Analyze the division

We have \(3.00\div8\). After getting \(0.3\) (since \(8\times0.3 = 2.4\)), we have a remainder of \(0.60\) (which is 60 hundredths). Now we need to divide \(0.60\) by \(8\).

Step2: Find how many times 8 goes into 60 hundredths

We know that \(8\times0.07 = 0.56\) (wait, no, let's do it properly. Wait, the dividend is \(3.00\), divisor \(8\). After \(0.3\) (which is \(8\times0.3 = 2.4\)), the remainder is \(3.00 - 2.4 = 0.60\). Now we bring down a zero (but it's already two decimal places, so we can think of \(0.60\) as 60 thousandths? No, wait, \(0.60\) is 60 hundredths. Wait, no, \(3.00\) is 3 dollars, 0 dimes, 0 pennies. Divided by 8. \(8\times0.3 = 2.4\) (2 dollars 4 dimes). Remainder is \(0.60\) (6 dimes). Now we convert 6 dimes to 60 pennies. So we have 60 pennies divided by 8. \(8\times7 = 56\) (pennies), so \(0.07\) (since 7 pennies is 0.07 dollars). Wait, so \(0.3 + 0.07 = 0.37\), with a remainder of \(60 - 56 = 4\) pennies, which is \(0.04\) dollars. But the question is about 60 hundredths divided by 8 ones? Wait, maybe the question is part of the long division. Let's focus on the long division.

Wait, the long division: \(3.00\div8\). Let's do it step by step.

1. \(8\) into \(3\) (ones place) is \(0\), so we put \(0\) and a decimal.
2. \(8\) into \(30\) (tenths place, since we have \(3.0\)): \(8\times3 = 24\), so \(0.3\), subtract \(24\) from \(30\) (tenths), remainder \(6\) tenths.
3. Bring down the \(0\) (hundredths place), making it \(60\) hundredths.
4. \(8\) into \(60\) hundredths: \(8\times7 = 56\) hundredths, so we put \(7\) in the hundredths place. So the quotient so far is \(0.37\), and the subtraction is \(56\) hundredths (since \(8\times0.07 = 0.56\)).
5. Remainder is \(60 - 56 = 4\) hundredths.

So in the long division, the first blank (the quotient's hundredths place) is \(7\), the subtraction line is \(0.56\) (wait, no, the second blank is the subtraction, which is \(8\times0.07 = 0.56\)? Wait, no, the first blank is the next digit in the quotient, which is \(7\) (since \(8\times7 = 56\) when we're in the hundredths place). The subtraction is \(56\) (hundredths), so the second blank is \(0.56\) (but written as \(56\) in hundredths, so \(0.56\) is \(56\) hundredths). Then the remainder is \(60 - 56 = 4\) hundredths, which would be brought down (but there's no more digits, so we can write it as \(0.375\) if we continue, but maybe the question is about 60 hundredths divided by 8.

Wait, 60 hundredths is \(0.60\), divided by 8 ones (which is 8). So \(0.60\div8 = 0.075\). But in the long division, when we have \(0.60\) (from the remainder after \(0.3\)) and we divide by 8, the next digit is \(7\) (since \(8\times0.07 = 0.56\)), so the quotient's hundredths place is \(7\), the subtraction is \(56\) (hundredths, so \(0.56\)), and the remainder is \(4\) (hundredths, which would be \(0.04\), and then we bring down a zero to make it \(40\) thousandths, and \(8\times5 = 40\), so the next digit is \(5\), making it \(0.375\)).

But the question is "What is 60 hundredths divided by 8 ones?" So \(0.60\div8\). Let's calculate that:

\(0.60\div8 = \frac{0.60}{8} = \frac{60}{800} = \frac{3}{40} = 0.075\).

In the long division, the first blank (the quotient's hundredths digit) is \(7\), the subtraction is \(56\) (hundredths, so \(0.56\) written as \(56\) in the subtraction, so the second blank is \(56\) (maybe as \(0.56\) but in the long division, it's \(56\) hundredths, so the subtraction line is \( - 0.56\), but written as \( - 56\) with the decimal places. Then the remainder is \(4\) hundredths, which would be \(04\) (so the last blank is \(04\) or \(4\) with a zero? Wait, maybe the long division is:

```
0.3 7
8)3.0 0
-2.4
----
0.6 0
-0.5 6
------
0.0 4
```

Wait, so the first blank (after \(0.3\)) is \(7\) (the hundredths digit), the subtraction is \(0.56\) (so the two blanks are \(5\) and \(6\)), and the remainder is \(0.04\) (so the last two blanks are \(0\) and \(4\) or \(4\) and \(0\)? Maybe the question is asking for the digit in the quotient (the first blank) which is \(7\), or the subtraction (the two blanks) which is \(56\), or the remainder. But the question says "What is 60 hundredths divided by 8 ones?" So \(0.60\div8 = 0.075\), but maybe in the context of the long division, the next digit is \(7\), and the subtraction is \(56\) (hundredths), and the remainder is \(4\) (hundredths).

Wait, let's re-express:

60 hundredths is \(0.60\), 8 ones is \(8\). So \(0.60\div8 = 0.075\). But in the long division, when we have \(0.60\) (after subtracting \(2.4\) from \(3.00\)), we divide \(0.60\) by \(8\). \(8\times0.07 = 0.56\), so we write \(7\) in the hundredths place, subtract \(0.56\) from \(0.60\), getting \(0.04\). So the quotient's next digit is \(7\), the subtraction is \(56\) (hundredths), and the remainder is \(4\) (hundredths, which is \(0.04\)).

But the question is "What is 60 hundredths divided by 8 ones?" So the answer is \(0.075\), but maybe in the context of the long division, the digit is \(7\) (for the hundredths place) or the result of \(60\) hundredths divided by \(8\) is \(7.5\) hundredths? Wait, no: \(60\) hundredths is \(0.60\), divided by \(8\) ones (which is \(8\)): \(0.60\div8 = 0.075\), which is \(7.5\) hundredths? Wait, \(0.075\) is \(7.5\) hundredths? No, \(0.075\) is \(75\) thousandths, or \(7.5\) hundredths (since \(1\) hundredth is \(0.01\), so \(7.5\times0.01 = 0.075\)). Ah, maybe that's the case. So \(60\) hundredths divided by \(8\) is \(7.5\) hundredths? Wait, \(60\div8 = 7.5\), so \(60\) hundredths divided by \(8\) ones is \(7.5\) hundredths, which is \(0.075\) in decimal.

But let's check the long division again. The dividend is \(3.00\), divisor \(8\).

- Step 1: \(8\) into \(3\) (ones) → \(0\), decimal point.
- Step 2: \(8\) into \(30\) (tenths) → \(3\) (since \(8×3=24\)), so \(0.3\), subtract \(24\) from \(30\) → remainder \(6\) tenths.
- Step 3: Bring down \(0\) (hundredths) → \(60\) hundredths.
- Step 4: \(8\) into \(60\) hundredths → \(7\) (since \(8×7=56\) hundredths), so we write \(7\) in the hundredths place, making the quotient \(0.37\), subtract \(56\) hundredths from \(60\) hundredths → remainder \(4\) hundredths.
- Step 5: Bring down another \(0\) (thousandths) → \(40\) thousandths.
- Step 6: \(8\) into \(40\) thousandths → \(5\) (since \(8×5=40\) thousandths), so we write \(5\) in the thousandths place, quotient \(0.375\), remainder \(0\).

So the first blank (after \(0.3\)) is \(7\) (the hundredths digit), the subtraction is \(56\) (hundredths, so the two blanks are \(5\) and \(6\)), and the remainder is \(4\) (hundredths, then \(40\) thousandths, etc.). But the question is "What is 60 hundredths divided by 8 ones?" So \(60\) hundredths is \(0.60\), \(8\) ones is \(8\). So \(0.60 ÷ 8 = 0.075\).

Answer:

\(0.075\) (or if the question is about the digit in the quotient, it's \(7\), but based on the division of \(0.60\) by \(8\), the result is \(0.075\))