Rational and irrational 5 questions
Sure! Here are five questions related to rational and irrational numbers, along with explanations on how to get the answers:
1. Is the square root of 2 rational or irrational?
To determine whether the square root of 2 is rational or irrational, we need to understand the concept of rational and irrational numbers. A rational number can be expressed as a fraction in the form of π/π, where π and π are integers, and π is not equal to 0. If the square root of 2 could be written as a fraction, it would mean that it can be expressed in the form of π/π. However, it has been proven that the square root of 2 cannot be expressed as a fraction, making it an irrational number.
2. Are all integers rational numbers?
Integers are a subset of rational numbers. A rational number can be expressed as a fraction, and integers can be expressed as fractions where the denominator is 1. For example, the integer 3 can be expressed as 3/1. Therefore, all integers are rational numbers.
3. Is the decimal representation of 1/3 a rational or irrational number?
To determine whether the decimal representation of 1/3 is rational or irrational, we need to compute the decimal representation of the fraction. When we divide 1 by 3, we get the decimal 0.3333..., where the digit 3 repeats infinitely. This repeating decimal indicates that 1/3 is a rational number.
4. Is the sum of a rational and irrational number always rational?
The sum of a rational and an irrational number is not always rational. In general, when you add a rational number and an irrational number, the result will be irrational. This is because an irrational number cannot be expressed as a fraction, and adding it to a rational number does not change its nature.
5. Is the product of a rational and an irrational number always irrational?
The product of a rational and an irrational number is not always irrational. In fact, the product of a rational and an irrational number can be either rational or irrational. It depends on the specific numbers being multiplied. If the rational number is zero or if the product can be expressed as a fraction, then it will be rational. However, in most cases, the product of a rational and an irrational number will be irrational.