The correct answers are
A. Irrational numbers are nonterminating; and C. Irrational numbers are nonrepeating.
Explanation:
Irrational numbers are numbers that cannot be written as rational numbers, or fractions.
Terminating decimals have a specific endpoint; this means we can find the place value of the last digit of the number and write it as a fraction (if it ends in the tenths place, it is a fraction over 10; if it ends in the hundredths place, a fraction over 100; etc.).
Repeating decimals can also be written as a fraction; for example, 0.3 repeating is 1/3; 0.6 repeating is 2/3; 0.1 repeating is 1/9; etc.
This means that irrational numbers must be nonrepeating and nonterminating.
The correct options are A and C because irrational numbers are nonterminating and nonrepeating.
Given:
Some statements for irrational numbers are written in decimal form.
Explanation:
Rational number: A rational number can be defined in the form of [tex]\dfrac{p}{q},q\neq 0[/tex]. Rational numbers are either terminating or repeating decimal numbers.
Examples: [tex]\dfrac{3}{5},2.555...,4.5[/tex] etc.
Irrational number: An irrational number cannot be defined in the form of [tex]\dfrac{p}{q},q\neq 0[/tex]. Irrational numbers are nonterminating and nonrepeating decimal numbers.
Examples: [tex]\sqrt{3},\pi ,1.35742784... [/tex] etc.
Therefore, the correct options are A and C.
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