The product of 14⋅10.2568 will be which of the following?(1 point)

Question

Responses

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

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

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

Radical, because there is a fraction and a decimal. 

Answer 1

To determine the nature of the product \(14 \cdot 10.2568\), let's analyze the options:

1. Integer, because both numbers are rational.

   • 14 is an integer, and 10.2568 is a decimal (which is also a rational number). The product of these two is \(14 \cdot 10.2568 = 143.596\), which is not an integer.

2. Rational, because both numbers are rational.

   • Both 14 and 10.2568 are rational numbers (they can be expressed as fractions). The product of two rational numbers is also rational, so this statement is correct.

3. Irrational, because one number is irrational.

   • Both numbers given are rational; therefore, this statement is incorrect.

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

   • The term "radical" typically refers to expressions involving roots, not the combination of fractions and decimals. This statement is incorrect.

Based on this analysis, the correct response is:

Rational, because both numbers are rational.