What is the decimal equivalent of `(1)/(10) +(11)/(100) +(111)/(1000) ?`

Options

A. 1.111
B. 0.111
C. 0.321
D. 0.1111

Answer

To find the decimal equivalent of the expression \( \frac{1}{10} + \frac{11}{100} + \frac{111}{1000} \), we can convert each fraction to its decimal form and then add them together.

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

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

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

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

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

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

So, we have:
```
0.100
+ 0.110
+ 0.111
--------
0.321
```

### Final Answer:
The decimal equivalent of \( \frac{1}{10} + \frac{11}{100} + \frac{111}{1000} \) is \( 0.321 \).

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