Is -4.17 rational or irrational and is 3.24037 rational or irrational and how can you tell the difference between them?
An irrational number is a real number that cannot be written as a simple fraction.
... and so any terminating decimal is rational.
To determine whether a number is rational or irrational, we need to understand the definitions of these terms.
A rational number can be expressed as a fraction or a ratio of two integers. In other words, it can be written as a/b, where a and b are integers and b is not equal to zero.
On the other hand, an irrational number is a number that cannot be expressed as a fraction or a ratio of two integers. Irrational numbers cannot be written in the form a/b, where a and b are integers and b is not equal to zero.
Now, let's analyze the numbers you provided:
1. -4.17: This number has a decimal component, but it can still be expressed as a fraction. To convert it into a fraction, we can multiply it by 100 to eliminate the decimal point and then simplify if necessary. In this case, -4.17 * 100 = -417/100. Since -417 and 100 are both integers and 100 is not zero, -4.17 can indeed be expressed as a fraction. Therefore, -4.17 is a rational number.
2. 3.24037: Similar to the previous example, this number is also a decimal. To determine whether it is rational or irrational, we must check if it can be expressed as a fraction. In this case, 3.24037 cannot be simplified into a fraction with integers for both the numerator and the denominator. Therefore, it cannot be expressed as a ratio of two integers, making it an irrational number.
To summarize, -4.17 is rational, while 3.24037 is irrational. The key difference lies in whether the numbers can be expressed as fractions or not.