Converting 0.123 to a Fraction in p/q Form and Understanding Bar Notation on 23
Introduction
In mathematics, converting decimal numbers to fractions is an essential skill, especially when working with ratios and proportions. In this article, we will explore how to convert 0.123 to a fraction in p/q form and understand the concept of bar notation on 23.
Converting 0.123 to a Fraction
To convert 0.123 to a fraction, we can use the following steps:
- Write the decimal as a fraction with a denominator of 1000: 0.123 = 123/1000
- Simplify the fraction: Divide both numerator and denominator by their greatest common divisor (GCD). In this case, the GCD is 1, so the simplified fraction is still 123/1000.
- Write the fraction in p/q form: 123/1000 = 41/333
So, 0.123 can be written as the fraction 41/333 in p/q form.
Understanding Bar Notation on 23
Bar notation, also known as the vinculum, is a horizontal line above a number that indicates repetition. In the context of 23, the bar notation denotes that the digits 23 are repeated indefinitely.
For example, 23̄ represents the decimal 0.232323... (where the pattern 23 is repeated infinitely).
In this case, 23 with a bar notation can be converted to a fraction as follows:
23̄ = 23/99
To understand why this is true, imagine dividing 23 by 99. The result is 0.232323..., which is the same as 23̄.
Conclusion
In this article, we have learned how to convert 0.123 to a fraction in p/q form (41/333) and understood the concept of bar notation on 23. These skills are essential in mathematics, particularly when working with ratios, proportions, and repetitive decimal patterns.
