Understanding Fractions and Decimals

Fractions and decimals are two different ways of representing numbers that are not whole. Both are essential in mathematics, science, engineering, and everyday life. Understanding how to convert between them is a fundamental mathematical skill.

What is a Fraction?

A fraction represents a part of a whole and consists of two numbers:

• Numerator: The top number, indicating how many parts you have
• Denominator: The bottom number, indicating how many equal parts the whole is divided into

Example: In the fraction 3/4, the numerator is 3 and the denominator is 4, meaning 3 parts out of 4 equal parts.

Converting Fractions to Decimals

To convert a fraction to a decimal, divide the numerator by the denominator.

Types of Decimal Representations

• Terminating Decimals: Have a finite number of digits (e.g., 1/4 = 0.25)
• Repeating Decimals: Have digits that repeat infinitely (e.g., 1/3 = 0.333...)
• Non-repeating Decimals: Continue infinitely without pattern (irrational numbers like π)

Converting Decimals to Fractions

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

1. Write the decimal as a fraction with 1 as the denominator
2. Multiply both numerator and denominator by 10 for each digit after the decimal point
3. Simplify the fraction by dividing by the GCD

Common Fraction-Decimal Equivalents

Fraction	Decimal	Percentage
1/2	0.5	50%
1/3	0.333...	33.33%
1/4	0.25	25%
1/5	0.2	20%
1/8	0.125	12.5%
1/10	0.1	10%
2/3	0.666...	66.67%
3/4	0.75	75%
3/5	0.6	60%
4/5	0.8	80%

Real-World Applications

Cooking and Baking

Recipes often use fractions for measurements, but digital scales use decimals:

Construction and Measurements

Rulers and measuring tapes often show fractions (1/16", 1/8"), while digital tools show decimals:

• 3/8 inch = 0.375 inches
• 5/16 inch = 0.3125 inches
• 7/8 inch = 0.875 inches

Finance and Money

Stock prices use decimals, but fractions are still used conceptually:

• 1/2 point = $0.50
• 1/4 point = $0.25
• 3/4 point = $0.75

Sports Statistics

Batting averages, completion percentages, and other stats convert fractions to decimals:

Working with Improper Fractions

An improper fraction has a numerator larger than the denominator (e.g., 7/4). These convert to decimals greater than 1:

• 7/4 = 1.75
• 5/3 = 1.666...
• 11/8 = 1.375

Mixed Numbers

A mixed number combines a whole number with a fraction (e.g., 2 1/4). To convert to decimal:

1. Convert the fraction part to decimal
2. Add to the whole number

Simplifying Fractions

Always simplify fractions when converting from decimals by finding the GCD:

Precision and Rounding

When converting fractions to decimals, you may need to round:

• 1/3 = 0.333... Often rounded to 0.33 or 0.333
• 2/3 = 0.666... Often rounded to 0.67 or 0.667
• 1/7 = 0.142857... Repeating pattern