If 7.71 + 7.071 + 7.0071 + ..... is equal to 21.79581, then what is the missing number?

Options

A. 7.00711
B. 7.00177
C. 0.00771
D. 0.070071

Answer

To find the missing number in the equation \( 7.71 + 7.071 + 7.0071 + x = 21.79581 \), we can follow these steps:

### Step 1: Add the known numbers
First, we need to add the three known numbers: \( 7.71 \), \( 7.071 \), and \( 7.0071 \).

\[ \begin{array}{r} 7.7100 \\ + 7.0710 \\ + 7.0071 \\ \hline \end{array} \]

Align the numbers by the decimal point and add them:

1. Start from the rightmost digit:
- \( 0 + 0 + 1 = 1 \)
2. Next column:
- \( 0 + 1 + 7 = 8 \)
3. Next column:
- \( 1 + 7 + 0 = 8 \)
4. Next column:
- \( 7 + 7 + 7 = 21 \) (write down 1 and carry over 2)
5. Finally, add the whole numbers:
- \( 7 + 7 + 7 + 2 = 23 \)

So, the total sum is \( 21.7881 \).

### Step 2: Set up the equation to find \( x \)
Now we can set up the equation to find \( x \):

\[ 21.7881 + x = 21.79581 \]

### Step 3: Solve for \( x \)
To find \( x \), we subtract \( 21.7881 \) from \( 21.79581 \):

\[ x = 21.79581 - 21.7881 \]

Align the numbers for subtraction:

\[ \begin{array}{r} 21.79581 \\ - 21.78810 \\ \hline \end{array} \]

Now perform the subtraction:

1. Start from the rightmost digit:
- \( 1 - 0 = 1 \)
2. Next column:
- \( 8 - 1 = 7 \)
3. Next column:
- \( 5 - 8 = 15 \) (borrow 1)
- \( 5 - 8 = 15 \) becomes \( 15 - 8 = 7 \)
4. Next column:
- \( 7 - 7 = 0 \)
5. Next column:
- \( 1 - 1 = 0 \)
6. Finally, the whole number part:
- \( 2 - 2 = 0 \)

So, \( x = 0.00771 \).

### Final Answer
The missing number \( x \) is \( 0.00771 \).

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