Solve: `2/10+2/1000-2/100+2/10000=`

Options

A. 0.1088
B. 0.1288
C. 1.0822
D. 0.1822

Answer

To solve the expression \( \frac{2}{10} + \frac{2}{1000} - \frac{2}{100} + \frac{2}{10000} \), we will follow these steps:

### Step 1: Identify the Denominators
The denominators in the expression are 10, 1000, 100, and 10000.

### Step 2: Find the Least Common Multiple (LCM)
The LCM of the denominators (10, 100, 1000, and 10000) is 10000. This will be our common denominator.

### Step 3: Convert Each Fraction to Have the Common Denominator
We will convert each fraction to have the denominator of 10000:

1. \( \frac{2}{10} = \frac{2 \times 1000}{10 \times 1000} = \frac{2000}{10000} \)
2. \( \frac{2}{1000} = \frac{2 \times 10}{1000 \times 10} = \frac{20}{10000} \)
3. \( \frac{2}{100} = \frac{2 \times 100}{100 \times 100} = \frac{200}{10000} \)
4. \( \frac{2}{10000} = \frac{2}{10000} \)

### Step 4: Rewrite the Expression
Now we can rewrite the expression with the common denominator:
\[ \frac{2000}{10000} + \frac{20}{10000} - \frac{200}{10000} + \frac{2}{10000} \]

### Step 5: Combine the Numerators
Now, we can combine the numerators:
\[ \frac{2000 + 20 - 200 + 2}{10000} = \frac{1822}{10000} \]

### Step 6: Convert to Decimal
To convert \( \frac{1822}{10000} \) to decimal, we can simply divide:
\[ \frac{1822}{10000} = 0.1822 \]

### Final Answer
Thus, the solution to the expression \( \frac{2}{10} + \frac{2}{1000} - \frac{2}{100} + \frac{2}{10000} \) is:
\[ \boxed{0.1822} \]