show that the following are rational number , by written then in the form a/b
7, 2x1/2 , 0.8
7/1
5/2
8/10
2x1/2 = 1/1
To show that a number is rational and to express it in the form a/b, we need to prove that it can be written as the quotient of two integers (a numerator and a denominator).
1. Number 7:
To express 7 as a fraction, we can write it as 7/1 since any whole number can be written as itself divided by 1. In this case, a = 7 and b = 1. Therefore, 7 is a rational number.
2. Number 2√1/2:
To express 2√1/2 as a fraction, we need to simplify the radical. The square root of 1 is 1, so we have 2/2, which reduces to 1/1. Therefore, a = 1 and b = 1. Thus, 2√1/2 is a rational number.
3. Number 0.8:
To express 0.8 as a fraction, we move the decimal point two places to the right to get 80/100. Then, we simplify it by dividing both numerator and denominator by their greatest common divisor, which is 20. So, 80/100 becomes 4/5. Therefore, a = 4 and b = 5. Thus, 0.8 is a rational number.
In conclusion, you can see that 7, 2√1/2, and 0.8 are rational numbers when written in the form a/b.