# Grade 8 - Number Theory #1

Andrew, Bob, Catherine, David and Emma are discussing about rational numbers and recurring decimals.

Andrew: Infinite decimals cannot be rational numbers.

Bob: Finite decimals and recurring decimals are all rational numbers.

Catherine: Natural numbers can always be expressed in the form of a recurring decimal, while there exists an integer that cannot be expressed in that form.

David: Some recurring decimals cannot be expressed in the form of a fraction having both of its numerator and denominator as rational numbers.

Emma: Fractions that have their denominator as a power of 10 must be rational numbers.

Andrew has number 1 on his shirt, Bob has number 2, Catherine has number 4, David has number 8 and Emma has number 16.

Add up all of the numbers on the shirts of the people whose statement is correct.

Detail:

• We don't consider expressions such as $$3.00000\cdots$$ and $$67.00000\cdots$$ as recurring decimals.

This problem is a part of <Grade 8 - Number Theory> series.

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