Find the First Difference

Which is greater: six point nine, or six point one two? The answer can feel backwards. But watch this... one tiny place-value check makes the larger number leap out.

Compare numbers from the greatest place value first. Line up the decimal points, so units sit under units, tenths under tenths, and hundredths under hundredths. Scan from left to right. The first place where the digits differ decides the order. Here, six point nine becomes six point nine zero. Both numbers have six units. At the tenths, nine is greater than one, so six point nine is greater than six point one two. Adding a zero at the end changes no value. Do not report the larger digit by itself. Say what it is worth. The nine means nine tenths, while the one means one tenth. Later digits cannot overturn a difference already found further left. On a number line, numbers further right are greater. This also handles negatives: minus two lies right of minus five.

Let's work through an example. Put these four numbers in ascending order, from smallest to largest: four point zero five, four point five, three point nine eight, and four point one five. Start with the units column. Three point nine eight has three units. Every other number has four units. Three units is smaller than four units, so three point nine eight comes first. We can now compare only the three numbers beginning with four. Write four point five as four point five zero. The units all match, so inspect the tenths. Zero tenths comes before one tenth, and one tenth comes before five tenths. Therefore the complete ascending order is: three point nine eight, four point zero five, four point one five, then four point five. Notice that we stopped at the first different place each time.

Remember: line up decimal points, compare the greatest place first, stop at the first difference, and name the place value, not just the digit. You can now order numbers with confidence!