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Q: When are the absolute value and the opposite of a rational number equal?

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When the number is 0.

When the number is non-positive.

Yes! When the number is negative, the absolute value of it'll be its opposite.

When the numbers are negative

The absolute value of a negative number is positive.

Because that is how the opposite is defined!

0

Because the opposite of 8 for example is -8 and 8+(-8) = 0

Only if the rational number is 0.

No, never.

the number 0 is always equal to its opposite

If a number is zero or positive, then its absolute value is equal to the number.

yes

The number 0.6666 is a rational number. Expressed as a fraction it is equal to 6666/10000.

1

Zero

No. If the rational number is not zero, then such a product is irrational.

No.

The way in which the binary functions, addition and multiplication, are defined on the set of rational numbers ensures that the set is closed under these two operations.

Yes, 100 is a rational number.A rational number is any number that can be expressed as the quotient a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number.

no all absolute values are positive

4.7 is already a rational number. If you mean as a mixed number, this is equal to 4 7/10 or four and seven tenths.

Assuming that the number ends at that third 5, yes, the number is rational - as it has a defined end-point. If the number is equal to 3.245 recurring, then no, the number will not be rational.

The requirement for a number to be a rational number is that it can be expressed as a ratio of two integers, where the denominator does not equal zero.

yes it is rational and is equal to 1 and 3/4