Question Video: Arranging a Set of Negative Decimals and Mixed Numbers Mathematics • 6th Grade

Arrange the following set of numbers in ascending order: −3 3/10, −3.61, −3.5.

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Video Transcript

Arrange the following set of numbers in ascending order: negative three and three-tenths, negative 3.61, and negative 3.5.

Ascending order is least to greatest, and we have three values. All three of the values are negative. Two of them are decimal numbers, and one is a mixed number. We have two choices. We could convert the mixed number to a decimal, or we could convert both of the decimal numbers into mixed numbers. Since two of the values are already in decimal form, let’s go ahead and convert this mixed number to a decimal number.

We know that the negative three will remain the whole-number portion. But how do we convert three-tenths to a decimal? Since this is a fraction out of 10, that’s a really simple procedure. We put a three in the tenths place so that we have negative 3.3. At this point, we have to be really careful because we’re ordering negative values. And when we order negative values, the least value will be the one that’s the furthest away from zero. And we know that the distance from zero is the absolute value of our number.

That means negative 3.61 is 3.61 units away from zero to the left. And it means that negative 3.5 is 3.5 units away from zero to the left. Negative 3.5 is closer to zero than negative 3.61, and negative 3.3 is the closest to zero of the three values. And that means to arrange them from least to greatest, we would list negative 3.61, negative 3.5, and then negative 3.3. However, for the final answer, it’s best to take negative 3.3 and put it back in the format we were given: negative three and three-tenths.

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