I found this question in one of my Algebra review books. Because it had the numbers in different forms, I was immediately drawn to it and wanted to figure it out. Because Algebra likes to simplify equations and expressions, and make things uniform, this was a good example of changing all the forms to the same standard. The question asked the students to put these numbers in least to most order.
5/8, 2.5 x 10-1, 150%,
I started by thinking of the numbers as people in line waiting to buy something.
I don't know about you, but as a left brained person, this looks like GREEK to me. But, if you notice, two of the numbers actually are "calling out" to you to convert them to decimals.
In a previous post entitled Left is for Lollipops and Right is for Rats I explain how to turn numbers into scientific notation. You can use that concept in reverse to change numbers back into decimal form.
Let's start with the 5/8. By fourth grade, students have learned this concept. Simply divide the numerator by the denominator. This gives the result of .625
Let's go to 150%. Changing percents to decimals is as easy as remembering that each of those 0's in the percent symbol represents a place to move the decimal. There are two zeros, so we are going to move the decimal two places. But, the left brained student is thinking, which way do I go? Which way do I go? Remind them that if they were in a STORE buying something, and it was on sale, they'd need to get to the front of the line to buy it. So, move the decimal (you) two spaces to the front of the line. The result is 1.5. Try this with 30 %, which they see sale signs for a lot. Move the decimal two places to the front of the line, and you get .30. ( I usually do ten percent in my head, then triple that.)
Let's move on the the number 2.5 x 10-1
Review the scientific notation post. Since this number is already in scientific notation form, we will do the OPPOSITE to convert it. Since we were already RIGHT with our negative exponent, we will go LEFT to convert it. We are moving our decimal 1 place because our little road sign says "exit 1 to the right." So since we are going LEFT, we are moving the decimal 1 place to the left with the result being .25.
Oh, my goodness, doesn't that square root look scarey? If it was the square root of four, you'd automatically think 2. If it was the square root of 9, you'd automatically think 3. But, what double times itself results in 2? Hey, it's been a long time. I don't have a chart. I Googled it. The answer is 1.414....
So the answer to the question of putting them in order from least to greatest is
.25, .625 , 1.414 , 1.5.
I have always reminded students that decimals are used most often in their lives for money. If they look at the terms above as money, they are easy to read.