# Comparing and Ordering Rational Numbers

When ordering rational numbers that aren’t in the same form, start by converting them all to the same form. **Remember, the larger a negative is, the smaller it is in value.**

## Ordering Rational Numbers

When ordering rational numbers that aren’t in the same form, start by converting them all to the same form. Let’s practice with this set of numbers here. **We’re going to order this set of numbers from least to greatest.** I’m going to start by converting all of these numbers into decimals.

One fourth. **To convert a fraction to a decimal, we divide our numerator by our denominator.** 1 divided by 4 is 0.25. 29%. To convert a percent to a decimal, divide by one hundred, or **simply move the decimal two places to the left.** That is 0.29. Our next number is already in decimal form, so I’ll just bring it down now. -0.8.

The square root of 16 is 4, since 4 times 4 is 16. -2 cubed means the opposite of 2 times 2 times 2. 2 times itself 3 times. 2 times 2 is 4. 4 times 2 is 8. The opposite of 8 is -8. Finally, we have the absolute value of -5. **Absolute value is the distance from zero.** -5 is five places from zero. The absolute value of -5 is 5.

Now that they’re all in the same form, we can order them from least to greatest. We’re going to start with our negative numbers, since those are smaller than our positive numbers. **Remember that the larger the negative, the smaller the number is.** -8 is a much bigger number, or- it’s a bigger negative, therefore it’s a smaller number.

-8 would be our smallest number. Starting with -8, after -8 would be our next negative number, -0.8. Then, we move to our positive numbers. Looking at our positive numbers, we’re going to start by looking at our whole numbers (our whole number values). Zero is our smallest whole number value, which means one of these numbers will come next.

If you look at the 10ths place, the 10ths place is also the same. Then, we’ve got to go one place further and look at the hundredths place to see which number would be next. This 0.25, the 5 is smaller than the 9, so 0.25 would be our next biggest number followed by 0.29. Then, we have our other two whole numbers, 4 and 5. 4 would be next followed by 5.

**The last thing we need to do is to put these numbers back in their original form.** -8 wasn’t the number we were given. That number was -2 cubed. We’re going to rewrite it as -2 cubed followed by -0.8, which is the original form. Then, we had 0.25, which was originally 1/4. After that, we had 0.29, which was originally 29%. Following that, we had 4, and four was originally the square root of 16. Finally, we have 5, and 5 was originally the absolute value of -5. Now we’ve ordered our numbers from least to greatest.