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You cannot be sure that what appear to be a non-repeating decimal does not in fact repeat after, say, a million places, in which case it would be equal to a certain fraction. If it really is non-repeating, then it is irrational, which is a fancy way of saying it does not represent a fraction using two integers.

Q: How can you verify that a particular non-repeating decimal is the equivalent of a certain fraction?

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... always equivalent to the fraction the certain number/64,and to the product (0.015625 x the certain number).

if you multiply a number by a certain factor and then divide it by the same factor you do not change anything. It is like multiplying by 1. If you multiply only the numerator you have changed the answer and it is not equivalent.

If you mean 45/60 then in its lowest terms it is 3/4

The only thing that you can be certain of is that the answer will be a number. It could be irrational or rational, it could be a proper fraction, integer or improper (mixed) fraction.

It is a rectangle. In the following sentence: A certain rectangle has length 8cm and width 5cm. The word "certain" could be replaced with "particular", or even omitted to have the same meaning.

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the word equivalent means equal to the certain fraction

... always equivalent to the fraction the certain number/64,and to the product (0.015625 x the certain number).

if you multiply a number by a certain factor and then divide it by the same factor you do not change anything. It is like multiplying by 1. If you multiply only the numerator you have changed the answer and it is not equivalent.

If you mean 45/60 then in its lowest terms it is 3/4

What is another word for certain? particular

The fraction or ratio of a sample possessing a certain trait is called a Proportion.

This hand gesture is "sign language" for a certain phrase. It is no accident that, viewed from the back of the hand, this particular gesture looks like a certain part of the male anatomy with it's attendant apendages. So to "flip off" some one is the equivalent of saying that particular phrase.

It tells what fraction of a radioactive sample remains after a certain length of time.

There is an infinite number of fractions for those numbers. However in simplest form it is 1/4 and 1/2 but you can multiply the numerator and denominator by any number to get an equivalent fraction. If you just need to list a certain number of these fractions you could multiply the top and the bottom times two to get an equivalent fraction and do it however many times you need fractions.

The only thing that you can be certain of is that the answer will be a number. It could be irrational or rational, it could be a proper fraction, integer or improper (mixed) fraction.

No. Certain is an adjective (particular, or for sure), and rarely a pronoun. But it cannot be a preposition.

It is adapted.