Irrational Rational
6.3
Irrational – 6 point 3
Rational – 6 point 3
4π
Irrational – 4 pi
Rational – 4 pi
12−−√
Irrational – square root of 12
Rational – square root of 12
15
Irrational – 1 fifth
Rational – 1 fifth
−3
Irrational – negative 3
Rational – negative 3
7.89¯¯¯¯¯
Irrational – 7 point repeating 8 9
Rational – 7 point repeating 8 9
100−−−√
Irrational – square root of 100
Rational – square root of 100
Rational – square root of 100
To determine whether a number is rational or irrational, we need to understand the definitions of these terms.
A rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero. In other words, a rational number can be written in the form of a fraction.
An irrational number, on the other hand, cannot be expressed as a ratio of two integers. It cannot be written as a simple fraction.
Now, let's analyze the given numbers one by one:
1. 6.3: This number can be expressed as 63/10, which is a ratio of two integers. Therefore, it is a rational number.
2. 4π: This is a multiplication of 4 and the irrational number π (pi). Since π is an irrational number, the product of 4π will also be irrational.
3. 12−−√: This represents the square root of 12. The square root of 12 is an irrational number because it cannot be expressed as a ratio of two integers.
4. 15: This number can be expressed as the fraction 15/1, which is a ratio of two integers. Therefore, it is a rational number.
5. −3: This number can be expressed as the fraction -3/1, which is a ratio of two integers. Therefore, it is a rational number.
6. 7.89¯¯¯¯¯: This number represents the repeating decimal 7.898989... Since it has a repeating pattern, it can be expressed as a fraction (e.g., 879/111), making it a rational number.
7. 100−−−√: This represents the square root of 100. The square root of 100 is equal to 10, which can be expressed as the ratio 10/1. Therefore, it is a rational number.
In conclusion, out of the given numbers, 4π and 12−−√ are irrational numbers, while the rest (6.3, 15, -3, 7.89¯¯¯¯¯, and 100−−−√) are rational numbers.