Write the fractions as decimal numbers:
281/ 125

Answer

To convert the fraction \( \frac{281}{125} \) into a decimal number, we will use the long division method. Here’s a step-by-step solution:

### Step 1: Set up the division
We will divide 281 by 125. This means we will write 281 inside the division bracket and 125 outside.

\[ \begin{array}{r|l} 125 & 281.000 \\ \end{array} \]

### Step 2: Determine how many times 125 fits into 281
We need to find the largest multiple of 125 that is less than or equal to 281.

- \( 125 \times 2 = 250 \) (this fits)
- \( 125 \times 3 = 375 \) (this is too much)

So, we will use 2.

### Step 3: Subtract to find the remainder
Now, subtract \( 250 \) from \( 281 \):

\[ 281 - 250 = 31 \]

### Step 4: Add a decimal point and a zero
Since 31 is smaller than 125, we need to add a decimal point and a zero to continue the division. This gives us 310.

\[ \begin{array}{r|l} 125 & 281.0 \\ \end{array} \]

### Step 5: Determine how many times 125 fits into 310
Now, we find how many times 125 fits into 310.

- \( 125 \times 2 = 250 \) (this fits)
- \( 125 \times 3 = 375 \) (this is too much)

So, we will use 2 again.

### Step 6: Subtract to find the new remainder
Subtract \( 250 \) from \( 310 \):

\[ 310 - 250 = 60 \]

### Step 7: Add another zero
Since 60 is still smaller than 125, we add another zero, making it 600.

\[ \begin{array}{r|l} 125 & 281.00 \\ \end{array} \]

### Step 8: Determine how many times 125 fits into 600
Now, we find how many times 125 fits into 600.

- \( 125 \times 4 = 500 \) (this fits)
- \( 125 \times 5 = 625 \) (this is too much)

So, we will use 4.

### Step 9: Subtract to find the new remainder
Subtract \( 500 \) from \( 600 \):

\[ 600 - 500 = 100 \]

### Step 10: Add another zero
Since 100 is still smaller than 125, we add another zero, making it 1000.

\[ \begin{array}{r|l} 125 & 281.000 \\ \end{array} \]

### Step 11: Determine how many times 125 fits into 1000
Now, we find how many times 125 fits into 1000.

- \( 125 \times 8 = 1000 \) (this fits perfectly)

### Step 12: Subtract to find the new remainder
Subtract \( 1000 \) from \( 1000 \):

\[ 1000 - 1000 = 0 \]

### Final Result
Since we have reached a remainder of 0, we can stop here. The decimal representation of \( \frac{281}{125} \) is:

\[ 2.248 \]

### Summary
Thus, \( \frac{281}{125} = 2.248 \).

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