Number 10
2 marks · EasyExplain why is an irrational number.
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is irrational because it cannot be written as a fraction , where , are integers and , and its decimal expansion is non-terminating and non-repeating.
Must show: states cannot be written as a fraction, mentions non-repeating, non-terminating decimal
Also accept: Not a perfect square, cannot be written as a ratio of two integers; its decimal is non-terminating and non-repeating.
Common mistakes: Saying it is irrational because it is a square root.; Not stating the fraction or decimal properties.
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Marking points
B1 · 1 mark · States that cannot be written as a fraction (a rational number) with integer numerator and denominator.
B2 · 1 mark · Mentions that the decimal expansion is infinite and non-repeating.
Worked solution
cannot be expressed as a fraction , where and are integers. Its decimal expansion is infinite and does not repeat, so it is irrational.