0.16 as a Rational Number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a and b, where b is non-zero. In this article, we will explore whether 0.16 can be expressed as a rational number.
What is 0.16?
0.16 is a decimal number that can be written in its fractional form as 16/100. However, this form is not yet in its simplest form.
Simplifying 0.16
To simplify 0.16, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 4. This gives us:
16 ÷ 4 = 4 100 ÷ 4 = 25
So, 0.16 can be simplified to 4/25.
Is 0.16 a Rational Number?
Now that we have simplified 0.16 to 4/25, we can see that it is indeed a rational number. This is because it can be expressed as the quotient of two integers, 4 and 25, where 25 is non-zero.
Properties of Rational Numbers
As a rational number, 0.16 possesses certain properties, including:
- Closure: The result of adding, subtracting, multiplying, or dividing two rational numbers is always a rational number.
- Commutativity: The order in which we add or multiply rational numbers does not change the result.
- Associativity: The order in which we add or multiply rational numbers can be changed without affecting the result.
- Distributivity: Rational numbers can be distributed across addition and subtraction.
Conclusion
In conclusion, 0.16 can be expressed as a rational number, specifically 4/25. As a rational number, it possesses certain properties that make it a fundamental concept in mathematics.
