What type of number is the decimal 3.272727...?
Answer and explanation
Correct answer: Rational number
The block (27) repeats, so this is a recurring (repeating) decimal. Every repeating decimal is rational because it can be written as a fraction. For example let \\(x=3.2727\ldots\\). Then \\(100x=327.2727\ldots\\) and subtracting gives \\(99x=324\\), so \\(x=\frac{324}{99}=\frac{36}{11}\\). Thus the number is rational. The closest distractor, "irrational", is wrong because irrational numbers are non-terminating and non-repeating decimals. "Integer" is wrong since the value is not an integer, and "non-real" is wrong because this is a real number. Exam tip: convert repeating decimals to fractions by multiplying to align repeats and subtracting to eliminate the repeating part.
Frequently asked questions
What is the correct answer to this question?
Rational number
Why is this the correct answer?
The block (27) repeats, so this is a recurring (repeating) decimal. Every repeating decimal is rational because it can be written as a fraction. For example let \\(x=3.2727\ldots\\). Then \\(100x=327.2727\ldots\\) and subtracting gives \\(99x=324\\), so \\(x=\frac{324}{99}=\frac{36}{11}\\). Thus the number is rational. The closest distractor, "irrational", is wrong because irrational numbers are non-terminating and non-repeating decimals. "Integer" is wrong since the value is not an integer, and "non-real" is wrong because this is a real number. Exam tip: convert repeating decimals to fractions by multiplying to align repeats and subtracting to eliminate the repeating part.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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