Which of the following is an irrational number?
1. 1,483,292. 2. 14/17. 3. 0.100100010000... 4. 0
#1.
0.100100010000 is irrational
It does not terminate, and it does not repeat
#2. closure means that the results belongs to the same set as the two addends
#3. integers are ration numbers, with a denominator of 1
#4. closure under addition
#5. -π + π = 0
Is 1.1 an irrational number?
Give us answers Pleeze
the answers are
1. D
2.B
3.B
4.C,D
5.C
6.B
Well, I have to say that option 4, "0," is definitely irrational. It's like trying to divide by zero – it just doesn't make any sense! It's kind of like when you ask your pet rock for advice and expect a response. Sometimes you just have to let go and move on to something that makes more sense, like a number that can be expressed as a fraction or a never-ending decimal.
To determine which of the following numbers is an irrational number, 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 and has an infinite decimal representation without a repeating pattern.
Let's analyze the given options:
1. 1,483,292: This number is a whole number. Whole numbers can be expressed as fractions with the denominator being 1, so it is a rational number.
2. 14/17: This number is a fraction. Fractions can be expressed as a ratio of two integers, so it is a rational number.
3. 0.100100010000... : This number is a decimal representation that repeats a pattern. Although the pattern may be infinite, it still repeats, so it can be expressed as a fraction. Thus, it is a rational number.
4. 0: This number is the whole number zero, and it can be expressed as a fraction (0/1). Therefore, it is a rational number.
Based on the analysis above, none of the given options is an irrational number.
Question 1
A) Which of the following is an irrational number?(1 point)
0
1,483,292
1427
0.100100010000...
Question 2
A) Which of the following is an example of closure?(1 point)
The equation 5−5=0 is an example of the natural numbers being closed under subtraction.
The equation 1.5+1.6=3.1 is an example of the rational numbers being closed under addition.
The equation 4−6=−2 is an example of the whole numbers being closed under subtraction.
The equation 1+0=1 is an example of the natural numbers being closed under addition.
Question 3
A) Which of the following statements about sets of numbers is true?(1 point)
All irrational numbers are integers.
All rational numbers are natural numbers.
All integers are rational numbers.
All integers are whole numbers.
Question 4
A) Without calculating, how do you know that the sum 221+331 is rational?(1 point)
Rational numbers are closed under addition, meaning that the sum of rational numbers is rational.
When adding fractions, the sum of two fractions is rational so long as both fractions are less than 1.
When adding fractions, the sum of two fractions is rational so long as both fractions are fully reduced.
The sum of any two positive numbers is rational.
Question 5
A)
Is the following statement true or false? If it is false, provide a counterexample.
The sum of two rational numbers is always rational, and the sum of two irrational numbers is always irrational.
(1 point)
The statement is false. A counterexample is the sum of the rational number 2 and the irrational number 0.3030030003....
The statement is false. A counterexample is the sum of the irrational numbers −π and π.
The statement is false. A counterexample is the sum of the rational numbers 47 and 29.
The statement is true.