Classify each number as Rational or Irrational using the drop down menu next to each number.
Number Classification
-15
3.67
25−−√
2π
4.8¯¯¯
12−−√
-15: Rational
3.67: Rational
25−−√: Irrational
2π: Irrational
4.8¯¯¯: Rational
12−−√: Irrational
Number Classification
-15 Rational
3.67 Rational
25−−√ Irrational
2π Irrational
4.8¯¯¯ Rational
12−−√ Irrational
To determine whether each number is rational or irrational, we need to understand the properties of each type of number.
Rational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not zero. In other words, rational numbers can be written in the form a/b, where a and b are integers.
Irrational numbers, on the other hand, cannot be expressed as a ratio of two integers. They are numbers that cannot be written as terminating or repeating decimals. Examples of irrational numbers include the square root of a non-perfect square and certain decimal numbers, such as π.
Now, let's classify each number:
-15: This is a rational number because it can be expressed as -15/1.
3.67: This is a rational number because it can be expressed as a fraction. To convert it to a fraction, we can write it as 3 67/100. Simplifying the fraction gives us 367/100.
25−−√: The square root of 25 is 5, which is a rational number. Therefore, 25−−√ is a rational number.
2π: π (pi) is an irrational number, and multiplying it by any rational number like 2 does not change its irrationality. Therefore, 2π is an irrational number.
4.8¯¯¯: The bar over the 8 indicates that the decimal repeats indefinitely. To convert this to a fraction, we can let x = 4.8¯¯¯. Then, multiplying both sides of the equation by 10, we get 10x = 48.8¯¯¯. Subtracting x from both sides of the equation, we get 10x - x = 48.8¯¯¯ - 4.8¯¯¯, which simplifies to 9x = 44. This means x = 44/9. Since 44 and 9 are both integers, 4.8¯¯¯ is a rational number.
12−−√: The square root of 12 is not a perfect square, and therefore, it is an irrational number. Thus, 12−−√ is an irrational number.