Question

Change 5.12 to decimal fraction
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Answer 1

To convert the mixed number 5.12 into a decimal fraction, you can follow these steps:

### Step 1: Understand the Structure
The mixed number 5.12 consists of a whole number (5) and a decimal part (0.12).

### Step 2: Convert the Whole Number to Decimal
The whole number is already in decimal format:
- Whole number = 5.00

### Step 3: Convert the Decimal Part
The decimal part is 0.12.

### Step 4: Combine the Whole Number and the Decimal Part
Now, we combine the whole number and the decimal part:
- 5.00 + 0.12 = 5.12

### Step 5: Represent as a Fraction
To express this as a fraction, we know that 5.12 can be written as:
- \( 5.12 = 5 + 0.12 \)

### Step 6: Convert Decimal to Fraction
The decimal 0.12 can be expressed as a fraction:
- 0.12 = \( \frac{12}{100} \) (since 12 is in the hundredths place).

### Step 7: Simplify the Fraction
Next, we simplify \( \frac{12}{100} \):
- The greatest common divisor (GCD) of 12 and 100 is 4.
- So, \( \frac{12 \div 4}{100 \div 4} = \frac{3}{25} \).

### Step 8: Combine Whole Number and Fraction
Now, we need to combine the whole number with the simplified fraction:
- 5 can be expressed as \( \frac{5 \times 25}{25} = \frac{125}{25} \).

### Step 9: Add the Two Fractions
Combine the whole number and the fractional part:
- \( 5.12 = 5 + 0.12 = \frac{125}{25} + \frac{3}{25} = \frac{125 + 3}{25} = \frac{128}{25} \).

### Final Answer
Thus, the decimal fraction equivalent of 5.12 is:
\[
\frac{128}{25}
\]