By actual division, express of the following as a terminating decimal:
`107/25`

Answer

To express \( \frac{107}{25} \) as a terminating decimal through actual division, follow these steps:

### Step 1: Set up the division
We need to divide 107 by 25. Write it as \( 107 \div 25 \).

### Step 2: Determine how many times 25 fits into 107
Look at how many times 25 can fit into 107.
- 25 fits into 107 a total of 4 times since \( 25 \times 4 = 100 \).

### Step 3: Subtract to find the remainder
Now, subtract 100 from 107:
\[ 107 - 100 = 7 \]
So, we have a remainder of 7.

### Step 4: Add a decimal point and a zero
Since 7 is less than 25, we need to add a decimal point to our quotient and bring down a zero, making it 70.

### Step 5: Divide again
Now, divide 70 by 25.
- 25 fits into 70 a total of 2 times since \( 25 \times 2 = 50 \).

### Step 6: Subtract again
Now, subtract 50 from 70:
\[ 70 - 50 = 20 \]
So, we have a new remainder of 20.

### Step 7: Bring down another zero
Again, since 20 is less than 25, we bring down another zero, making it 200.

### Step 8: Divide one more time
Now, divide 200 by 25.
- 25 fits into 200 a total of 8 times since \( 25 \times 8 = 200 \).

### Step 9: Subtract to find the final remainder
Subtract 200 from 200:
\[ 200 - 200 = 0 \]
So, there is no remainder left.

### Final Result
Putting it all together, we find that:
\[ \frac{107}{25} = 4.28 \]
Thus, \( 107 \div 25 = 4.28 \), which is a terminating decimal.

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