Understanding Fractions and Decimals: 1/5 as a Decimal
Fractions and decimals are two ways to represent parts of a whole. Understanding how to convert between them is a key skill in math. Let's explore how to convert the fraction 1/5 into its decimal equivalent.
What is a Fraction?
A fraction represents a part of a whole. It consists of two numbers separated by a line. The top number is called the numerator and represents the number of parts we are considering. The bottom number is called the denominator and represents the total number of parts in the whole.
What is a Decimal?
A decimal is another way to represent a part of a whole. It uses a decimal point to separate the whole number part from the fractional part. Each digit after the decimal point represents a power of ten. For example, 0.1 represents one-tenth, 0.01 represents one-hundredth, and so on.
Converting 1/5 to a Decimal
To convert 1/5 to a decimal, we can use the following methods:
1. Division Method:
- Divide the numerator by the denominator: Divide 1 by 5.
- The result is the decimal equivalent: 1 ÷ 5 = 0.2
2. Fraction to Decimal Conversion:
- Recognize that the denominator, 5, is a factor of 10. We can multiply the numerator and denominator by 2 to get an equivalent fraction with a denominator of 10:
- (1 x 2) / (5 x 2) = 2/10
- The equivalent fraction with a denominator of 10 can be easily written as a decimal: 2/10 = 0.2
Why does this work?
Both methods are based on the same principle: dividing the numerator by the denominator essentially represents dividing the whole into equal parts and taking the desired number of those parts. In the case of 1/5, we are dividing the whole into 5 equal parts and taking one of those parts.
Important Note:
Not all fractions can be converted to terminating decimals. Fractions with denominators that are not factors of 10 will result in repeating decimals. For example, 1/3 converts to 0.3333... (the 3 repeats infinitely).
Conclusion
The fraction 1/5 is equivalent to the decimal 0.2. Understanding the relationship between fractions and decimals is crucial for solving various mathematical problems and interpreting data effectively.