Sure! A quick check on rational numbers can help you understand their different forms. Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. Here are some forms of rational numbers:
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Fraction Form: A rational number can be written as \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b \neq 0\).
- Example: \(\frac{3}{4}\), \(-\frac{7}{2}\)
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Decimal Form: A rational number can also be expressed in decimal form. This can be either terminating or repeating.
- Terminating: 0.75 (which is \(\frac{3}{4}\))
- Repeating: 0.333... (which represents \(\frac{1}{3}\))
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Integer Form: Any whole number is a rational number because it can be expressed as itself over 1.
- Example: 5 can be written as \(\frac{5}{1}\), and -3 as \(-\frac{3}{1}\)
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Mixed Number Form: A mixed number is a whole number combined with a proper fraction.
- Example: \(2 \frac{1}{4}\) is a rational number as it can be converted to \(\frac{9}{4}\)
Quick Check Questions:
- Convert the fraction \(\frac{5}{8}\) into decimal form.
- Is the number 0.2 a rational number? If yes, convert it into fraction form.
- Convert the mixed number \(3 \frac{2}{5}\) into an improper fraction.
- Identify if \(-1.75\) is a rational number and express it in fraction form.
- What decimal representation would be expected from the fraction \(\frac{2}{3}\)?
Answers:
- \(\frac{5}{8} = 0.625\)
- Yes, 0.2 is a rational number and can be expressed as \(\frac{2}{10}\) or simplified to \(\frac{1}{5}\).
- \(3 \frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{17}{5}\)
- Yes, \(-1.75\) is a rational number, and in fraction form, it is \(-\frac{7}{4}\).
- The decimal representation of \(\frac{2}{3}\) is approximately \(0.666...\) (repeating).
Let me know if there's anything else you would like to review!
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