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Lesson 43: Working with Decimals (Tenths and Hundredths)
We've learned the basics of fractions. In this lesson, we'll talk about special fractions which involve 10 parts and 100 parts.
You've learned that if you eat 3 out of 8 pizza slices, you've eaten 3/8 of the pie, which is read as "three eighths." In this lesson you'll learn a special way of representing fractions which involve 10 parts and 100 parts.
Let's pretend that the pizza was cut into 10 slices, and you ate 7 of them. You ate 7/10, which is read as "seven tenths." Be careful, it is not seven tens, it is seven tenths. There is a very big difference.
In our system of math, we have special place values for tenths, just like we have special place values for ones, tens, and hundreds. This is explained more below.
There is a special way of writing 7/10. We can write "0.7". The 0 is actually in the ones place. We don't have any ones, since we didn't eat any whole pies. We just ate a fraction of one. The seven is in the tenths place, and to the left of the tenths place, we put a decimal point. That tells us that we are now moving into the world of fractional parts. Working with decimals in this way comes up again and again in math.
Let's say you cut a square pizza pie into 100 tiny equal bite-sized pieces, and let's say that you ate 3 of those. We can say that you ate 3/100, or three hundredths of the pie. Not three hundreds, but three hundredths. We can write this as a decimal as "0.03". This means we have no ones, we have no tenths, but we have three hundredths. The 3 is in the hundredths place.
Let's look at a chart to see how place value works.
| Hundreds | Tens | Ones | (Decimal Point) | Tenths | Hundredths |
| 100 | 10 | 1 | . | 0.1 | 0.01 |
Let's say you ate 27 of those bite sized pieces described above. We would actually write that as "0.27". The 20 part of the 27 actually represents two-tenths of the pie, because you ate 20 pieces out of 100. Then you ate 7 more pieces, so that is 7/100, or 7 hundredths. That's why we have a 2 in the tenths place, and a 7 in the hundredths place.
Understand that two tenths is the same as 20 hundredths. Each tenth of the pie, is actually 10 of the hundredths, so two tenths is twenty of the hundredths. I suggest placing 100 counters into a 10x10 grid, and experiment to see how to divide the counters into tenths and hundredths. This topic can be a bit tricky, but it comes up almost constantly in math, so make sure you feel comfortable with it.
Make sure that you understand that 0.39 is a smaller number than 0.93. The first number has a 3 in the tenths place (and some hundredths), and the second number has a 9 in the tenths place (and some hundredths). Since the second number has more tenths, it is a bigger number. Also understand that a number such as 0.7 can be represented as .7 (omitting the 0 before the decimal point), as well as 0.70 (adding the 0 to show that there are no hundredths). Later you'll learn much more about how to work with decimal numbers like these.
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