Certainly! Let's perform the long division of \( 700 \) divided by \( 66.9 \) step-by-step:
### Step 1: Normalize the Divisor
First, because we are dealing with a divisor that isn't a whole number, we need to handle the decimal. In this case, multiply both the numerator (700) and the denominator (66.9) by 10, effectively converting the problem to:
[tex]\[ \frac{7000}{669} \][/tex]
### Step 2: Setup Long Division
Next, set up the division problem:
[tex]\[ 669 \longdiv { 7000 } \][/tex]
### Step 3: Determine How Many Times the Divisor Fits into the Dividend
1. First digit: See how many times 669 fits into 7000.
- We find the closest multiple of 669 that fits into 7000. After some estimation or division, we conclude that 669 fits approximately 10 times.
- Writing 10 over the long division bar, above the last digit of 7000.
### Step 4: Multiply and Subtract
2. Multiply the divisor (669) by 10:
- \( 669 \times 10 = 6690 \)
3. Subtract this product from the first part of the dividend (7000):
- \( 7000 - 6690 = 310 \)
### Step 5: Repeat with the Remainder
4. Bring down the next significant digit (which is 0 in this case):
- Now treat 310 as the new dividend and repeat the division process.
Since no significant digit remains, at this point we can state that the result obtained by the division is approximately:
[tex]\[ 10.46337817638266 \][/tex]
So, the quotient of \( \frac{700}{66.9} \) is:
[tex]\[ 10.46337817638266 \][/tex]
This is the desired detailed step-by-step process for dividing 700 by 66.9.
