When ordering decimals, place value is very important. We’re going to begin by looking at the numbers to the left of the decimal. So, if we look at our numbers to the left of the decimal, we’re ordering these numbers from least to greatest.
Then the smallest number to the left of our decimal is this whole number, -3. -3 is the smallest whole number out of our whole set. So, -3.68 would be our first decimal, least to greatest.
Next lesson is Fractions of a Whole, both lessons are part of the practice tests.[divider]The following transcript is provided for your convenience.[divider]
So, we’re going to look for our next biggest, which means we’re still looking at our whole numbers. So, again, looking at our whole numbers, the next whole number, the next biggest would be 0.056, because the whole number 0 is greater than -3, but it’s smaller than these whole numbers 2 and 3. So, our next number would be 0.056.
So, again, we’re going to look for the next greatest whole number. So, looking at our whole numbers again, 3, 3, 2, and 2, 2 is going to be our next number, 2 is smaller than 3, but we have 2 of them. We have 2 numbers with the whole number 2 in front. So, we’ve got to move to our next place, our tenths place, and look at the tenths place to see which of our numbers would be the next in our line from least to greatest. So, looking at the tenths place, this number, 2.2344 has a smaller number in the tenths place than our other decimal does. So, since we’re ordering from least to greatest, this number would be next, followed by 2.3872, since it was the next because of our whole numbers.
So, we’re done with our twos, moving on to our next whole number. These two are the last ones I have, and again, they have that same whole number.
So, then, we’d move to the tenths place, to compare our tenths place, and see which one is smaller. Looking at our tenths place, again, they have the same number. So, still, we don’t know which one’s going to come next. So, we move on then and look at the hundredths place. Looking at hundredths place, they’re still the same, so right now, we still can’t tell which one’s bigger, which one’s smaller. So, we move one more place over, to the thousandths place. Looking at the thousandths place for this number, we have a 2 in the thousandths place. By looking at 3.57, there is no number in the thousandths place. When you’re missing a number after your decimal, it’s always 0. In fact, you could fill in as many zeroes after each one of these numbers as you wanted to. It doesn’t change your number. So, since this number has a 0 in the thousandths place, and this decimal has a 2 in the thousandths place, that means this number is smaller, so it’d be our next number in the series. So, 3.57, followed finally by 3.572.
So, when you’re ordering decimals, start by looking at your whole number, and ordering that from least to greatest. If your whole numbers are the same, like they were here, then look at the tenths place, and see which one is smaller in your tenths place. If, like, in these numbers, you have the same whole number, the same number in the tenths place, then you move to the hundredths. If those are the same, you move to the thousandths, and so on and so on, until you find the numbers from least to greatest.
Next lesson is Fractions of a Whole, both lessons are part of the practice tests.