Convert the following rational numbers into decimals:
`(5)/(8)`

Answer

To convert the rational number \( \frac{5}{8} \) into a decimal, we will perform the division of 5 by 8 step by step.

### Step 1: Set up the division
We need to divide 5 by 8. Since 5 is less than 8, we will first write it as a decimal. We can express 5 as 5.000 (adding decimal places).

### Step 2: Perform the division
Now, we divide:
- 8 goes into 50 (the first two digits of 5.000) 6 times because \( 8 \times 6 = 48 \).
- Write down 6 after the decimal point.

### Step 3: Subtract
Now, subtract 48 from 50:
- \( 50 - 48 = 2 \).

### Step 4: Bring down the next digit
Bring down the next 0 (from 5.000), making it 20:
- Now we need to see how many times 8 goes into 20.
- 8 goes into 20 two times because \( 8 \times 2 = 16 \).
- Write down 2 after the 6.

### Step 5: Subtract again
Now, subtract 16 from 20:
- \( 20 - 16 = 4 \).

### Step 6: Bring down the next digit
Bring down the next 0 (from 5.000), making it 40:
- Now we need to see how many times 8 goes into 40.
- 8 goes into 40 five times because \( 8 \times 5 = 40 \).
- Write down 5 after the 62.

### Step 7: Final subtraction
Now, subtract 40 from 40:
- \( 40 - 40 = 0 \).

Since we have a remainder of 0, we can conclude our division.

### Final Result
Thus, the decimal form of \( \frac{5}{8} \) is \( 0.625 \).

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