The product of 1/4⋅10.2568

Question

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

Radical, because there is a fraction and a decimal.
Radical, because there is a fraction and a decimal.

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

Irrational, because one number is irrational.
Irrational, because one number is irrational.

An integer, because both numbers are rational.

Answer 1

To determine the nature of the product \( \frac{1}{4} \cdot 10.2568 \), we will analyze the numbers involved.

1. Fraction \( \frac{1}{4} \): This is a rational number, as it can be expressed as the ratio of two integers (1 and 4).
2. Decimal \( 10.2568 \): This is also a rational number, as it can be expressed as a fraction (for instance, \( 10.2568 = \frac{102568}{10000} \)).

The product of two rational numbers is always a rational number.

Thus, the product \( \frac{1}{4} \cdot 10.2568 \) is rational.

The correct response is:

Rational, because both numbers are rational.