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The product of 1/4⋅10.2568

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.

An integer, because both numbers are rational.
An integer, because both numbers are rational.

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

Rational, because both numbers are rational.

1 answer

To determine the nature of the product \( \frac{1}{4} \cdot 10.2568 \), let's analyze the components:

  1. Rational Numbers:
    • \( \frac{1}{4} \) is a rational number (a fraction).
    • \( 10.2568 \) is also a rational number, as it can be expressed as a fraction (specifically \( \frac{102568}{10000} \)).

The product of two rational numbers is also a rational number. Therefore, the product \( \frac{1}{4} \cdot 10.2568 \) is rational.

So, the correct response is:

Rational, because both numbers are rational.