The product of 1/4⋅10.2568

Question

1
4
⋅
10.2568
will be which of the following?(1 point)
Responses

An integer, because both numbers are rational.
An integer, because both numbers are rational. - no response given

Rational, because both numbers are rational.
Rational, because both numbers are rational. - correct

Irrational, because one number is irrational.
Irrational, because one number is irrational. - no response given

Radical, because there is a fraction and a decimal.

Answer 1

To determine the product of \( \frac{1}{4} \) and \( 10.2568 \), we can perform the multiplication:

\[ \frac{1}{4} \cdot 10.2568 = 2.5642 \]

Now, analyzing the nature of this product:

1. Rational Numbers: Both \( \frac{1}{4} \) and \( 10.2568 \) are rational numbers. A rational number is any number that can be expressed as the quotient of two integers (where the denominator is not zero).

2. Product of Rational Numbers: The product of two rational numbers is always a rational number.

Thus, \( 2.5642 \) is also a rational number.

Therefore, the correct response is:

Rational, because both numbers are rational.