Which decimals are irrational numbers? Select two answers.
A. π
B. 1 1/3
C. 8/526
D. 0.212212221…
E. 5/9
I'm going to say C and D. I'm not entirely sure though. Please help!
any fraction is rational.
D is irrational.
So that ;eaves only A.
Read up on pi for further information.
By the way, π, or pi, is 3.14159265359.
The correct answers are A (π) and D (0.212212221…).
An irrational number is a decimal that cannot be expressed as a fraction or a ratio of two integers.
π (pi) is an irrational number that represents the ratio of a circle's circumference to its diameter. It is approximately equal to 3.1415926535897932384626433...
The decimal 0.212212221… is also an irrational number because it is a non-repeating and non-terminating decimal. It cannot be expressed as a fraction or a ratio of two integers.
On the other hand, options B and E (1 1/3 and 5/9) are rational numbers because they can be expressed as fractions of two integers.
Option C (8/526) is a rational number as well, since it can be expressed as a simplified fraction.
To determine which decimals are irrational numbers, we need to understand what irrational numbers are.
Irrational numbers are decimal numbers that cannot be expressed as a fraction of two integers, meaning they cannot be written as a ratio or a fraction. Irrational numbers have an infinite number of non-repeating digits after the decimal point.
Now let's go through the options you provided:
A. π (pi) is an irrational number. It is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is approximately 3.14159, but it goes on infinitely without repeating.
B. 1 1/3 can be expressed as a fraction, which is 4/3. Therefore, it is not an irrational number.
C. 8/526 can be reduced to a fraction, which is 4/263. Therefore, it is not an irrational number.
D. 0.212212221... appears to be a repeating decimal, with the sequence "212" repeating. Repeating decimals can always be expressed as a fraction, so it is not an irrational number.
E. 5/9 can be expressed as a fraction, so it is also not an irrational number.
Based on the explanations above, the two decimals that are irrational numbers are A. π (pi) and D. 0.212212221…