Understanding Decimal to Mixed Fraction Conversion

What is a Decimal?

A decimal is a way of writing a number that includes a decimal point. It represents a whole number plus a fractional part. For example, 3.75 represents 3 whole units plus 75 hundredths.

What is a Mixed Fraction?

A mixed fraction (or mixed number) is a whole number plus a proper fraction. For example, 3 3/4 is a mixed fraction that represents 3 whole units plus 3/4 of a unit.

Converting Decimal to Mixed Fraction

To convert a decimal to a mixed fraction, we follow these steps:

1. Separate the whole number part from the decimal part.
2. Convert the decimal part to a fraction.
3. Simplify the fraction if possible.
4. Combine the whole number with the fraction.

Formula

There isn't a single formula for this conversion, but we can express the process mathematically:

\[d = w + f\]

Where:

• \(d\) is the decimal number
• \(w\) is the whole number part
• \(f\) is the fractional part (0 ≤ f < 1)

Calculation Steps

Let's convert 3.75 to a mixed fraction:

1. Separate whole and decimal parts:

   Whole part: 3

   Decimal part: 0.75

2. Convert 0.75 to a fraction:

   \[0.75 = \frac{75}{100}\]

3. Simplify the fraction:

   \[\frac{75}{100} = \frac{3}{4}\]

4. Combine whole number and fraction:

   \[3\frac{3}{4}\]

Example with Visual Representation

Let's visualize 3.75 as a mixed fraction:

This diagram shows 3 whole units plus 3/4 of a unit, representing 3.75 visually.