Correct Answers:
B: 6
D: - 7/6
E: -6
F: 0
You are given a list of numbers {-6, 6, - 7/6, 2.73773777…, 0, square root of 43}. Which numbers are rational? Irrational?
Which numbers are rational? Select all that apply.
A. 2.73773777…
B. 6
C. Square root of 43
D. - 7/6
E. -6
F. 0
I’m not trying to cheat I just need help explaining how to do this.
4 answers
Unless x is a perfect square, √x is irrational
is 43 a perfect square?
well, 6^2 = 36
7^2 = 49
so 43 cannot be a perfect square
any repeating decimal is rational
.737 = 737/999
is 43 a perfect square?
well, 6^2 = 36
7^2 = 49
so 43 cannot be a perfect square
any repeating decimal is rational
.737 = 737/999
rational means result of dividing two integers
A. is NOT - it looks like a repeating decimal at first but is not because number of sevens changes
B. 6/1 = 6, Yes
C. No. By the way the square root of any PRIME number fails
D yes, negative is ok
E yes
F yes, but remember you are not allowed to DIVIDE by 0
A. is NOT - it looks like a repeating decimal at first but is not because number of sevens changes
B. 6/1 = 6, Yes
C. No. By the way the square root of any PRIME number fails
D yes, negative is ok
E yes
F yes, but remember you are not allowed to DIVIDE by 0
Any number which can be expressed as a fraction is rational
(notice the "ratio" part in "rational")
This includes all natural and whole numbers, all integers, and all fractions
all terminating decimals, and all decimals have a repeat in the sequence of decimals
e.g. 4.56 , 72.484848...
Irrationals, (not rational) are all those real numbers that cannot be expressed as an exact fraction. This would include all square roots of positive numbers except those square roots of perfect squares
e.g. √5 is irrational, but √36 is rational
so clearly C), √43 is irrational, as is A) 2.73773777... . In the decimal number there will never be an actual repeat of the decimals since we seem to be adding a 7 in each round, so it never repeats.
(notice the "ratio" part in "rational")
This includes all natural and whole numbers, all integers, and all fractions
all terminating decimals, and all decimals have a repeat in the sequence of decimals
e.g. 4.56 , 72.484848...
Irrationals, (not rational) are all those real numbers that cannot be expressed as an exact fraction. This would include all square roots of positive numbers except those square roots of perfect squares
e.g. √5 is irrational, but √36 is rational
so clearly C), √43 is irrational, as is A) 2.73773777... . In the decimal number there will never be an actual repeat of the decimals since we seem to be adding a 7 in each round, so it never repeats.