Converting 0.12 and 3 Bar in p/q Form
In mathematics, converting decimals to fractions and vice versa is an essential skill. In this article, we will explore how to convert 0.12 and 3 bar (repeating decimal) to their equivalent forms in p/q.
What is p/q Form?
In mathematics, p/q form refers to a fraction where p and q are integers, and q is non-zero. This form is used to represent a rational number, which is a number that can be expressed as the ratio of two integers.
Converting 0.12 to p/q Form
To convert 0.12 to p/q form, we can follow these steps:
- Divide 0.12 by 1 to get the fraction: 0.12/1
- Multiply both numerator and denominator by 100 to eliminate the decimal point: (0.12 × 100)/(1 × 100) = 12/100
- Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD): 12/100 = 3/25
Therefore, 0.12 in p/q form is 3/25.
Converting 3 Bar to p/q Form
A 3 bar, also known as a repeating decimal, is a decimal that has a repeating pattern of digits. To convert a 3 bar to p/q form, we can follow these steps:
- Let x = 3.bar (the repeating decimal)
- Multiply both sides by 10 to get: 10x = 33.bar
- Subtract x from both sides to get: 9x = 30
- Divide both sides by 9 to get: x = 30/9
- Simplify the fraction by dividing both numerator and denominator by their GCD: 30/9 = 10/3
Therefore, 3 bar in p/q form is 10/3.
Conclusion
In this article, we have learned how to convert 0.12 and 3 bar to their equivalent forms in p/q. By following the steps outlined above, we can convert any decimal or repeating decimal to its fraction form. This skill is essential in mathematics, especially in algebra, geometry, and other higher-level math subjects.
