1. Which of the following numbers is a rational?
A. 4/5 ***
B. square root of 27
C. 4.02002000200002...
D. Square root of 31
2. Which type of number is shown below?
0.313311333111...
A. repeating decimal
B. rational ***
C. irrational
D. terminating decimal
3. Select all the rational numbers from the list.
A. square root of 2 ***
B.8.21221112221111 ***
C. 8.333333333... ***
D. square root of 80
E. square root of 25 ***
4. Select all the irrational numbers from the list.
A. square root of 16
B.square root of 7
C. 813.1 ***
D. -9 ***
E. 8.070070007...
5. Which of the following numbers is
irrational?
A. square root of 36
B. 1/5
C. square root of 60
D.6.3
PLEASE HELP!!!
#1 ok
#2 Since A and B are equivalent, and D is obviously false, it must be C.
#3 only C and E
Since 2 is not a perfect square, its square root must be irrational
B is not a repeating decimal. Its groups of digits keep getting longer, and it does not terminate.
#4 also B. Since you got A right, I'm surprised that you also picked B.
1^2 = 1
2^2 = 4
3^2 = 9
So 7 is not a perfect square.
#5 all except A are irrational, since only 36 is a perfect square.
1. To determine which of the given numbers is rational, we need to understand what a rational number is. A rational number is a number that can be expressed as a fraction of two integers, where the denominator is not zero.
Looking at the options:
A. 4/5 - This is a fraction of two integers, so it is a rational number.
B. Square root of 27 - The square root of 27 is not a fraction, so it is not a rational number.
C. 4.02002000200002... - This is a repeating decimal, but it can be expressed as a fraction, so it is a rational number.
D. Square root of 31 - The square root of 31 is not a fraction, so it is not a rational number.
Therefore, the rational number among the given options is A. 4/5.
2. To determine the type of number shown as 0.313311333111..., we need to understand the different types of numbers.
A repeating decimal is a decimal in which a pattern of digits repeats indefinitely.
A rational number is a number that can be expressed as a fraction of two integers, where the denominator is not zero.
An irrational number is a number that cannot be expressed as a fraction of two integers.
A terminating decimal is a decimal number that ends after a specific number of decimal places.
Looking at the given number, 0.313311333111..., it has a repeating pattern of digits (313). This means it is a repeating decimal, which is a type of rational number.
Therefore, the type of number shown is A. repeating decimal.
3. To select all the rational numbers from the list, we need to determine which numbers can be expressed as fractions of integers.
Looking at the options:
A. Square root of 2 - The square root of 2 cannot be expressed as a fraction of two integers, so it is not a rational number.
B. 8.21221112221111 - This number is not given as a fraction, but it is a repeating decimal and can be expressed as a fraction, so it is a rational number.
C. 8.333333333... - This is a repeating decimal and can be expressed as a fraction, so it is a rational number.
D. Square root of 80 - The square root of 80 cannot be expressed as a fraction of two integers, so it is not a rational number.
E. Square root of 25 - The square root of 25 is a whole number, which can be expressed as a fraction, so it is a rational number.
Therefore, the rational numbers from the list are B. 8.21221112221111, C. 8.333333333..., and E. square root of 25.
4. To select all the irrational numbers from the list, we need to determine which numbers cannot be expressed as fractions of integers.
Looking at the options:
A. Square root of 16 - The square root of 16 is a whole number, which can be expressed as a fraction, so it is a rational number.
B. Square root of 7 - The square root of 7 cannot be expressed as a fraction of two integers, so it is an irrational number.
C. 813.1 - This number is given as a finite decimal, so it can be expressed as a fraction, making it a rational number.
D. -9 - -9 is a whole number, which can be expressed as a fraction, so it is a rational number.
E. 8.070070007... - This is a repeating decimal and can be expressed as a fraction, so it is a rational number.
Therefore, the irrational number from the list is B. square root of 7.
5. To determine which of the given numbers is irrational, we need to understand what an irrational number is.
An irrational number is a number that cannot be expressed as a fraction of two integers.
Looking at the options:
A. Square root of 36 - The square root of 36 is a whole number, which can be expressed as a fraction, so it is a rational number.
B. 1/5 - This is a fraction of two integers, so it is a rational number.
C. Square root of 60 - The square root of 60 cannot be expressed as a fraction of two integers, so it is an irrational number.
D. 6.3 - This number is given as a finite decimal, so it can be expressed as a fraction, making it a rational number.
Therefore, the irrational number among the given options is C. square root of 60.