Which number is rational 2.1010010001 0.8974512 1.2547569 5.3333333 – Exploring the concept of rational numbers, this analysis delves into the question of whether the given numbers 2.1010010001, 0.8974512, 1.2547569, and 5.3333333 qualify as rational numbers. Through a comprehensive examination of their properties and decimal representations, we will determine their rational or irrational nature.
Identify Rational Numbers
Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. In other words, rational numbers are numbers that can be written in the form a/b, where a and b are integers and b ≠ 0.
Examples of rational numbers include:
- 0
- 1/2
- -3/4
- 5
- -100
To identify rational numbers, we can use the following properties:
- Every integer is a rational number.
- The sum, difference, product, and quotient of two rational numbers is a rational number.
- The reciprocal of a rational number is a rational number.
Analyze Given Numbers: Which Number Is Rational 2.1010010001 0.8974512 1.2547569 5.3333333
| Number | Rationality |
|---|---|
| 2.1010010001 | TBD |
| 0.8974512 | TBD |
| 1.2547569 | TBD |
| 5.3333333 | TBD |
Determine Rationality
To determine if a number is rational, we can use the following step-by-step method:
- Express the number as a decimal.
- Determine if the decimal is terminating or non-terminating.
- If the decimal is terminating, then the number is rational.
- If the decimal is non-terminating, then the number is irrational.
Terminating decimals are decimals that end after a finite number of digits. For example, 0.5 is a terminating decimal because it ends after one digit. Non-terminating decimals are decimals that do not end after a finite number of digits. For example, 0.12345678910111213… is a non-terminating decimal because it does not end after any finite number of digits.
Analyze Decimal Representations
| Number | Decimal Representation | Terminating or Non-Terminating | Rationality |
|---|---|---|---|
| 2.1010010001 | TBD | TBD | TBD |
| 0.8974512 | TBD | TBD | TBD |
| 1.2547569 | TBD | TBD | TBD |
| 5.3333333 | TBD | TBD | TBD |
Based on the analysis of the decimal representations, we can determine the rationality of the given numbers:
- 2.1010010001 is a non-terminating decimal, therefore it is irrational.
- 0.8974512 is a non-terminating decimal, therefore it is irrational.
- 1.2547569 is a non-terminating decimal, therefore it is irrational.
- 5.3333333 is a terminating decimal, therefore it is rational.
FAQ Summary
What is a rational number?
A rational number is a number that can be expressed as a fraction of two integers, where the denominator is not zero.
How can we identify rational numbers?
Rational numbers can be identified by their decimal representations. If a decimal representation is terminating (ends) or non-terminating but repeating, then the number is rational.
