Unit 1: Working with Decimals
Topic B: Reading & Writing Decimals
Remember the place value chart of whole numbers? Complete the following exercise for a refresher.
Exercise 1
352 is the number on the first line of the chart below. The 3 is in the hundreds spot, the 5 is in the tens spot, and the 2 is in the ones spot.
Place the following numbers on the place value chart:
- 4984
- 836466
- 70834
| Thousands | Ones | |||||
|---|---|---|---|---|---|---|
| Hundred thousands | Ten thousands | One thousand | Hundreds | Tens | Ones | . (decimal point) |
| 3 | 5 | 2 | . | |||
Answers to Exercise
Check with your instructor to see if you have placed the numbers in the chart correctly.
Turning a Decimal into Words
Have you ever wondered what goes to the right of the decimal in a place value chart? That is where the decimal numbers go! (The parts of the whole.)
Here is a place value chart for decimals:
| Hundreds | Tens | Ones | Decimal | Tenths | Hundredths | Thousandths | Ten thousandths | Hundred thousandths |
|---|---|---|---|---|---|---|---|---|
| 3 | . | 4 | 5 | 3 | ||||
| 0 | . | 9 | 6 |
See the words in to the right of the decimal point? They look different than the usual whole number words you are used to. These are all the names for the decimal places. You will see them in the next lesson.
The first number on the chart above is 3.453. We say “Three point four five three” or “Three and four hundred fifty-three thousandths.”
- 3 is in the ones spot
- 4 is in the tenths spot
- 5 is in the hundredths spot
- 3 is in the thousandths spot
The second number is 0.96. We say “Zero point nine six” or “Zero and ninety six hundredths.”
- 0 is in the ones spot
- 9 is in the tenths spot
- 6 is in the hundredths spot
Tenths Place
Common fractions with a denominator of 10 are written as a decimal with one place to the right of the decimal point. This is the tenths place.
We often shorten “places to the right of the decimal point” to “decimal places.” We can say that tenths have one decimal place.
- [latex]\frac{6}{10}[/latex] = 0.6 = six tenths
- [latex]\frac{3}{10}[/latex] = 0.3 three tenths
Exercise 2
- [latex]\frac{4}{10}[/latex] = 0.4 = four tenths
- [latex]\frac{1}{10}[/latex] = 0.1 = one tenth
- [latex]\frac{2}{10}[/latex] = =
- [latex]\frac{9}{10}[/latex] = =
- [latex]\frac{7}{10}[/latex] = =
- Now enter each common fraction in the place value chart below. The first one is done for you. Please show this to your instructor once you are finished to make sure you are on the right track.
| Hundreds | Tens | Ones | Decimal | Tenths | Hundredths | Thousandths | Ten thousandths | Hundred thousandths |
|---|---|---|---|---|---|---|---|---|
| 0 | . | 4 | ||||||
Answers to Exercise 2
- 0.4, four tenths
- 0.1, one tenth
- 0.2, two tenths
- 0.9, nine tenths
- 0.7, seven tenths
Decimals with one digit to the right of the decimal point have an unwritten denominator of ten. This means that the whole thing is broken into 10 equal parts. Each part is called a tenth.
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