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What is a rational number?
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A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, where the numerator p is an integer, and the denominator q is a non-zero integer.
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Can a whole number be considered a rational number? Why or why not?
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Yes, a whole number is a rational number because it can be expressed as a fraction with the whole number as the numerator and 1 as the denominator.
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Is the number 0 a rational number?
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Yes, 0 is a rational number because it can be represented as 0/1.
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Are all integers rational numbers?
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Yes, all integers are rational because any integer z can be written as z/1.
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Give an example of a negative rational number.
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Examples of negative rational numbers include -3/4 or -2.
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Explain how to determine if a number is rational.
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A number is rational if it can be written as a fraction a/b where a and b are integers, and b is not zero.
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Is the number π (pi) a rational number? Why or why not?
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No, pi is not a rational number because it is an irrational number; it cannot be expressed as a simple fraction or decimal.
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What is the decimal representation of every rational number like?
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The decimal representation of every rational number either terminates or repeats.
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Explain whether 1.25 is a rational number and why.
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Yes, 1.25 is a rational number because it can be expressed as a fraction 5/4.
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Are fractions like 2/3 considered rational numbers?
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Yes, fractions like 2/3 are considered rational numbers as both the numerator and denominator are integers, and the denominator is not zero.
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Is the square root of 4 a rational number? Explain.
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Yes, the square root of 4 is rational because it equals 2, which can be expressed as 2/1.
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How do rational numbers behave with addition and subtraction?
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Rational numbers are closed under addition and subtraction, meaning if you add or subtract two rational numbers, the result is also a rational number.
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Explain how multiplication affects rational numbers.
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Rational numbers are closed under multiplication; multiplying two rational numbers always results in another rational number.
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What is the result of dividing two rational numbers?
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The result of dividing one rational number by another (except division by zero) is also a rational number.
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Describe how to convert a repeating decimal into a fraction.
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To convert a repeating decimal to a fraction, set the repeating decimal to a variable, then multiply by a power of 10 that moves the repeating part next to the decimal point, subtract, and solve for the fraction.
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