Convert into decimal `2 1/25`

Options

A. 2.4
B. 2.04
C. 2.004
D. none of these

Answer

To convert the mixed fraction \(2 \frac{1}{25}\) into a decimal, 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 into an improper fraction, we use the formula:

\[ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator}\right) + \text{Numerator} \]

For \(2 \frac{1}{25}\):
- Whole Number = 2
- Numerator = 1
- Denominator = 25

Calculating the improper fraction:

\[ 2 \times 25 + 1 = 50 + 1 = 51 \]

So, \(2 \frac{1}{25} = \frac{51}{25}\).

### Step 2: Divide the numerator by the denominator
Now we need to divide 51 by 25 to convert it into a decimal.

\[ 51 \div 25 \]

Performing the division:
- 25 goes into 51 two times (since \(25 \times 2 = 50\)).
- Subtract \(50\) from \(51\) to get a remainder of \(1\).

Now we have:

\[ 51 \div 25 = 2 \quad \text{(with a remainder of 1)} \]

### Step 3: Add a decimal point and continue dividing
Since we have a remainder, we need to add a decimal point and a zero to continue the division.

Now we treat the remainder \(1\) as \(10\) (by adding a decimal point and a zero):

\[ 10 \div 25 \]

25 goes into 10 zero times. So we write \(0\) after the decimal point.

Next, we add another zero to the remainder \(10\) to make it \(100\):

\[ 100 \div 25 \]

25 goes into 100 four times (since \(25 \times 4 = 100\)).

Now we have:

\[ 51 \div 25 = 2.04 \]

### Final Answer
Thus, the decimal representation of \(2 \frac{1}{25}\) is:

\[ \boxed{2.04} \]

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