What is the answer of 75 divided by 12 in rational number in decimal?
The correct answer and explanation is:
Answer:
75 divided by 12 = 6.25
This is the decimal form of the rational number.
Explanation (300 words):
A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. That is, a rational number can be written as: ab,where a and b are integers and b≠0.\frac{a}{b}, \quad \text{where } a \text{ and } b \text{ are integers and } b \ne 0.
In the case of 75 divided by 12, we are essentially evaluating the rational number: 7512\frac{75}{12}
To convert this to decimal form, we divide the numerator by the denominator: 75÷12=6.2575 \div 12 = 6.25
This division is exact, meaning there is no remainder. Therefore, the decimal 6.25 is a terminating decimal, which is a type of rational number because it can be written as a fraction: 6.25=625100=2546.25 = \frac{625}{100} = \frac{25}{4}
This also confirms that 6.25 is rational.
Why is 6.25 a Rational Number?
Any decimal that terminates or repeats is a rational number. In contrast, irrational numbers have non-terminating and non-repeating decimals, like π or √2.
Since 6.25 terminates, it is a rational number and can be expressed in fractional form.
Final Answer:
75 ÷ 12 = 6.25, and 6.25 is a rational number because it can be written as a ratio of two integers.