which is a irationaal?
a. 0.117117117......**
b.0.8596876205....
c.0.812812812812....
d. 0.605605605.....
what is 0.32 written as a fraction in simplest form?
a.32/100***
b.8/25
c.100/32
d 16/25
plz help
since there is a repeat of 117 in the decimal, it is rational.
take 117/999 on your calculator
your second answer of 32/100 is not in lowest terms as asked for
32/100 = 8/25
thanks!!
To determine which number is irrational among a, b, c, and d, we need to understand the definition of an irrational number. An irrational number is a number that cannot be expressed as the quotient (or ratio) of two integers, which means it cannot be written as a fraction in simplest form.
Let's analyze each option:
a. 0.117117117......: This number is a repeating decimal. It can be expressed as 117/999, which is a fraction. Therefore, it is not irrational.
b. 0.8596876205....: We cannot determine if this number is irrational just by looking at the given decimal. To check if it is rational or irrational, we would need to see if the decimal repeats or terminates.
c. 0.812812812812....: Similar to option (a), this is a repeating decimal. It can be expressed as 812/999, which is a fraction. Hence, it is not irrational.
d. 0.605605605.....: Similarly, this is a repeating decimal. It can be written as 605/999, which is a fraction. Therefore, it is not irrational.
From the options provided, it appears that (b) might be an irrational number since it is the only one not explicitly identified as a fraction.
For the second question, we need to express 0.32 as a fraction in simplest form:
0.32 can be written as 32/100. However, this fraction can be simplified further. Both the numerator and denominator can be divided by their greatest common divisor, which is 4 in this case.
When we divide 32 and 100 by 4, we get 8 and 25 respectively.
Thus, 0.32 written as a fraction in simplest form is 8/25, which corresponds to option (b).
I hope this explanation helps you understand how to identify irrational numbers and simplify fractions!