Fill in the blanks so that the statement is true: Decimal 8.125 is equal to the fraction _______.

Answer

To convert the decimal 8.125 into a fraction, we can follow these steps:

### Step 1: Identify the decimal
The decimal we have is 8.125.

### Step 2: Write the decimal as a fraction
To convert the decimal to a fraction, we can express it as:
\[ 8.125 = \frac{8125}{1000} \]
This is because there are three digits after the decimal point (125), which means we will have 1000 in the denominator.

### Step 3: Simplify the fraction
Next, we need to simplify the fraction \(\frac{8125}{1000}\). We can do this by finding the greatest common divisor (GCD) of 8125 and 1000.

1. **Finding the GCD**:
- The prime factorization of 8125 is \(5^3 \times 13\).
- The prime factorization of 1000 is \(10^3 = 2^3 \times 5^3\).
- The common factor is \(5^3\).

2. **Dividing both the numerator and denominator by the GCD**:
\[ \frac{8125 \div 125}{1000 \div 125} = \frac{65}{8} \]

### Step 4: Final answer
Thus, the fraction equivalent of the decimal 8.125 is:
\[ \frac{65}{8} \]

### Step 5: Convert to mixed fraction (optional)
If we want to express \(\frac{65}{8}\) as a mixed fraction:
1. Divide 65 by 8, which gives 8 with a remainder of 1.
2. So, we can write it as:
\[ 8 \frac{1}{8} \]

### Final Answer
The decimal 8.125 is equal to the fraction \(\frac{65}{8}\) or as a mixed fraction \(8 \frac{1}{8}\).

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