The decimal equivalent to `(1)/(10) + (11)/(100) + (111)/(1000)` is :

Options

A. 11.11
B. 0.123
C. 0.321
D. 0.1111

Answer

To find the decimal equivalent of the expression \((1)/(10) + (11)/(100) + (111)/(1000)\), we can follow these steps:

### Step 1: Convert each fraction to its decimal form
1. **Convert \((1)/(10)\)**:
\[ \frac{1}{10} = 0.1 \]

2. **Convert \((11)/(100)\)**:
\[ \frac{11}{100} = 0.11 \]

3. **Convert \((111)/(1000)\)**:
\[ \frac{111}{1000} = 0.111 \]

### Step 2: Add the decimal values together
Now, we will add the decimal values we found:
\[ 0.1 + 0.11 + 0.111 \]

To add these, we can align them by their decimal points:
```
0.111
+ 0.110
+ 0.100
---------
```

### Step 3: Perform the addition
Starting from the rightmost column:
- In the thousandths place: \(1 + 0 + 0 = 1\)
- In the hundredths place: \(1 + 1 + 0 = 2\)
- In the tenths place: \(0 + 1 + 1 = 2\)

So, we have:
\[ 0.111 + 0.110 + 0.100 = 0.321 \]

### Final Answer
The decimal equivalent of \((1)/(10) + (11)/(100) + (111)/(1000)\) is:
\[ \boxed{0.321} \]

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