Is -16×3.14 rational or irrational
The Correct Answer and Explanation is:
The number (-16 \times 3.14 = -50.24) is rational because it can be expressed as a fraction.
To determine whether (-16 \times 3.14) is rational or irrational, let’s first calculate the result of the multiplication and then assess its rationality.
- Multiplying the numbers:
[
-16 \times 3.14 = -50.24
]
The result is (-50.24). - Understanding Rational and Irrational Numbers:
- Rational numbers are numbers that can be expressed as a fraction, meaning they can be written in the form (\frac{a}{b}), where (a) and (b) are integers, and (b \neq 0). Rational numbers include all integers, fractions, and finite or repeating decimals.
- Irrational numbers are numbers that cannot be expressed as a fraction of two integers. These numbers cannot be written as a simple fraction and have non-repeating, non-terminating decimal expansions. Examples of irrational numbers include (\pi), (e), and the square root of non-perfect squares, such as (\sqrt{2}).
- Analyzing the result:
The number (-50.24) is a decimal number with a finite number of digits after the decimal point (two decimal places). Any number with a finite decimal expansion can be written as a fraction. For example, we can express (-50.24) as:
[
-50.24 = \frac{-5024}{100}
]
This is a fraction where both the numerator ((-5024)) and denominator ((100)) are integers. - Conclusion:
Since (-50.24) can be written as a fraction, it is a rational number.
Therefore, the number (-16 \times 3.14 = -50.24) is rational because it can be expressed as a fraction.