There are lot of numbers in between zero and one . They can be in the form of fractions, decimal numbers,irrational number. Few numbers can be 0.2, 0.3, 0.4 and many more.
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Fractions and decimals
All numbers between negative one and zero are negative. When you multiply a number by a negative it becomes negative. Also, all numbers between negative one and zero are decimals. When you multiply a number by a decimal it becomes smaller. Thus, when you multiply a rational number by a number between negative one and zero, it becomes smaller and negative.
Once again, if you're talking about whole numbers, then negative integers and zero. But since fractions and decimals are numbers, and are not integers, anything between negative infinity to 1 are before one. So fractions and/or decimals between 1 and zero, such as 1/2, 0.9, and anything between negative infinity and zero, such as -1024, -6/13, 69.029.
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One of the numbers being zero makes no difference.