Fraction to Decimal and Decimal to Fraction Converter

Fractions and decimals are two ways to represent and work with rational numbers. In various mathematical calculations and everyday situations, we often need to convert between these two representations. This article will discuss the conversion process between fractions and decimals, including their descriptions, formulas, and examples with tables.

Fraction to Decimal Conversion

A fraction is a representation of a rational number in the form of a/b, where a is the numerator and b is the denominator. To convert a fraction to a decimal, simply divide the numerator by the denominator:

Decimal = Numerator / Denominator

Example
Convert the fraction 3/4 to a decimal:

Decimal = 3 / 4 = 0.75

So, the decimal representation of 3/4 is 0.75.

Fraction to Decimal Conversion Table

Decimal to Fraction Conversion

A decimal is a number that represents a rational number using the decimal numeral system. Decimal numbers can be finite or repeating. To convert a decimal to a fraction, follow these steps:

• Determine the place value of the last digit of the decimal (e.g., tenths, hundredths, etc.).
• Write the decimal as a fraction with the denominator equal to the place value (e.g., 10 for tenths, 100 for hundredths, etc.).
• Simplify the fraction, if possible, by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by the GCD.

Example
Convert the decimal 0.75 to a fraction:

1. The last digit of 0.75 is in the hundredths place.
2. Write 0.75 as a fraction: 75/100.
3. Simplify the fraction by finding the GCD of 75 and 100 (which is 25), and dividing both the numerator and denominator by the GCD: (75 / 25) / (100 / 25) = 3/4. So, the fractional representation of 0.75 is 3/4.

Fraction to Decimal Conversion Table

FractionDecimal.com provides an overview of fraction to decimal, decimal to fraction conversion, along with descriptions, formulas, and examples with tables. You can use these concepts to better understand the relationships between fractions, decimals and percentages to perform conversions in various mathematical and real-world applications.

Fractions and Decimals

Fractions: Fractions represent parts of a whole. They consist of a numerator (the number above the line) and a denominator (the number below the line). For example, in the fraction 3/4, the numerator is 3 (three parts) and the denominator is 4 (four equal parts making up the whole).

Decimals: Decimals are another way to represent parts of a whole or numbers. They are based on powers of 10 and are expressed in terms of tenths, hundredths, thousandths, and so on. For instance, 0.5 represents 5 tenths or half of a whole, while 0.25 stands for 25 hundredths.

Conversion between Fractions and Decimals:

1. Converting Fractions to Decimals:
   To convert a fraction to a decimal, divide the numerator by the denominator. For example:
   3/4 = 3 ÷ 4 = 0.75
2. Converting Decimals to Fractions:
   To convert a decimal to a fraction, identify the place value of the decimal and use it as the numerator. The denominator will be a power of 10 corresponding to the decimal's place value. For instance:
   0.6 = 6/10 = 3/5 (Simplified)
3. Common Fraction to Decimal Equivalents:
   Some fractions have common decimal equivalents, such as 1/2 = 0.5, 1/4 = 0.25, 1/5 = 0.2, and so on. Recognizing these equivalents can be helpful for quick conversions.

Understanding the relationship between fractions and decimals is crucial in various mathematical operations, including addition, subtraction, multiplication, and division. Moreover, knowing how to convert between them provides flexibility in problem-solving and facilitates comparisons between different representations of numbers.

Mastering these concepts and conversions helps in everyday situations as well. For instance, when dealing with measurements or money, decimals are often used, but fractions might be more practical for certain tasks or estimations.

Practicing with exercises involving both fractions and decimals can significantly enhance one's mathematical skills, fostering a deeper understanding of numbers and their representations.

More Fraction to Decimal and Decimal to Fraction Examples

Converting Fractions to Decimals

Example 1: Converting 5/8 to a decimal:
5 ÷ 8 = 0.625

Example 2: Converting 7/10 to a decimal:
7 ÷ 10 = 0.7

Example 1: Converting 3/4 to a decimal:
3 ÷ 4 = 0.75

Example 2: Converting 2/5 to a decimal:
2 ÷ 5 = 0.4

Converting Decimals to Fractions

Example 1: Converting 0.25 to a fraction:
0.25 = 25/100 = 1/4 (Simplified)

Example 2: Converting 0.8 to a fraction:
0.8 = 8/10 = 4/5 (Simplified)

Example 3: Converting 0.125 to a fraction:
0.125 = 125/1000 = 1/8 (Simplified)

Example 1: Converting 0.6 to a fraction:
0.6 = 6/10 = 3/5 (Simplified)

Example 2: Converting 0.375 to a fraction:
0.375 = 375/1000 = 3/8 (Simplified)