Decimal Notation: Clarifying the Use of 0.5 vs. .5

In mathematics, the representation of numbers in decimal form is a fundamental concept. A common discussion in schools and educational settings revolves around the appropriate use of decimal notation, specifically whether 1/2 is expressed as 0.5 or .5. This article aims to clarify the standard practices in decimal notation and provide insights into the correct usage.

The Debate: 0.5 vs. .5

A student once argued that 1/2 as a decimal should be written as .5 because 0.5 is not a number. This misunderstanding has led to a series of questions and clarifications. Let's explore the nuances of this discussion.

Standard Notations in Mathematics

Firstly, it is essential to recognize that in mathematics, 1/2 written as a decimal is 0.5. This notation is widely accepted and used globally. The representation of decimals, including the placement of the decimal point, follows specific rules and conventions that are standardized for ease of understanding and consistency.

Thousand Separators

There is a common misconception that the comma (,) is used as a separator for numbers larger than a thousand. However, this practice is outdated. The international standard today is to use a space to separate thousands, or leave a space between groups of thousands. For example, instead of writing 324973322722, it is more readable as 3 249 7 332 2 722 or 3249 7332 2722.

Use of Thousands Separators

The issue of thousands separators is more nuanced. While there is no strict rule mandating their use, certain authorities recommend the use of spaces instead of commas. This recommendation is based on the clarification by the International Bureau of Weights and Measures, the International Union of Pure and Applied Chemistry, the American Medical Association (AMA), and the Metrication Board, among others.

The international standard, as per these authorities, dictates that a fixed space should be used instead of a comma to separate groups of thousands. Therefore, the correct way to write 32,497,332,272 is 3249 7332 2722 or 3 249 7 332 2 722. Both 3249 and 3.249 are incorrect.

Usage of 0.5 vs .5

The use of 0.5 versus .5 is another topic of debate. The student’s concern about the omission of the integer portion is valid, but his argument that 0.5 is not a number is incorrect. In official and standardized contexts, 0.5 and .5 are both correct, but .5 is more commonly seen in the USA to save space.

For instance, the United States Medical Association (AMA) and other official sources recommend the use of .5 to abbreviate 0.5. However, it is crucial to recognize that this is a regional and practical preference, and it is not universal. In academic and professional settings, 0.5 is generally preferred for clarity and consistency.

Standard View from a Calculator

The standard view can be easily verified using a calculator. When you divide 1 by 2, the result is definitively 0.5. This is a consistent and widely accepted representation in mathematical and scientific communities.

Global Variations in Decimal Notation

It is important to recognize that decimal notation varies across different regions and contexts. Over five different types of decimal separators are found in common and historical use. The practice of insisting on a local and personal preference as the "correct" one is limiting and can lead to misunderstandings.