Convert each of the following fractions into a decimal :
`4(11)/125`

Answer

To convert the mixed fraction \( 4 \frac{11}{125} \) into a decimal, we can follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
A mixed fraction consists of a whole number and a proper fraction. To convert it to an improper fraction, we multiply the whole number by the denominator and add the numerator.

\[ 4 \frac{11}{125} = \frac{(4 \times 125) + 11}{125} \]

Calculating the multiplication and addition:

\[ 4 \times 125 = 500 \]
\[ 500 + 11 = 511 \]

Thus, we have:

\[ 4 \frac{11}{125} = \frac{511}{125} \]

### Step 2: Convert the improper fraction to a decimal
To convert the fraction \( \frac{511}{125} \) to a decimal, we can perform the division of the numerator by the denominator.

\[ 511 \div 125 \]

Performing the division:

1. 125 goes into 511 four times (since \( 125 \times 4 = 500 \)).
2. Subtract 500 from 511 to get a remainder of 11.
3. Now, we can express this as \( 4 \) with a remainder of \( 11 \).

To continue, we can add a decimal point and a zero to the remainder:

\[ 110 \div 125 \]

125 goes into 110 zero times, so we write \( 0 \) after the decimal point. Now we have:

\[ 4.0 \]

Next, we can add another zero to the remainder:

\[ 1100 \div 125 \]

125 goes into 1100 eight times (since \( 125 \times 8 = 1000 \)). Subtracting 1000 from 1100 gives us a remainder of 100.

Continuing with the division:

\[ 1000 \div 125 \]

125 goes into 1000 eight times (since \( 125 \times 8 = 1000 \)). Subtracting gives us a remainder of 0.

Thus, we can conclude that:

\[ \frac{511}{125} = 4.088 \]

### Final Answer:
The decimal representation of \( 4 \frac{11}{125} \) is \( 4.088 \).

---