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Tenths - place value
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The base 10 number system - place value
The digit 6 in the number 6,702 actually has the value 6,000 and the digit 7 actually signifies the value 700. This is why our number system is called also a place value system, because the value of a digit (like 6 or 7 in our example) depends on its placement within the number. In other words, the digit 6 in 6702 does not mean six but six thousand because the six is placed in the thousands' place. The place of a digit determines its value. The comma between thousands and hundreds is added as a separator for easier reading. In some countries an empty space is used instead: 6,702 is written as 6 702. |
Example problem types
1. Write these numbers the normal way.
| a. 7 + 40 + 300 | d. | 9000 + 5 + 30 |
| c. 60 + 400 + 2 | f. | 200 + 2 + 50 |
2. Write the following numbers the normal way.
| a. 7 × 1 | f. | 6 × 100 + 5 × 10 |
| e. 5 × 100 + 6 × 1 | j. | 5 × 1000 + 5 × 100 + 9 × 10 + 2 × 1 |
Look at the different place values again.
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Tenths
Read the word "and" in place of the decimal point, and use the word "tenths" for the digit after the decimal point. The other way of reading is just to read the decimal point as "point" and then read the individual digits with number words. |
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If there is no whole number part, some people omit the zero and write 0.7 as .7 etc. |
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3. Fill in the missing parts and read aloud.
| Number | Broken down | Read | ||||
| .5 = 0.5 |
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five tenths | OR | point five/zero point five | ||
| 1.8 |
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one and eight tenths | OR | one point eight | ||
| 607.6 | ||||||
| 1,330.3 | ||||||
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Note: the word decimal can mean TWO things: Thus we can say that the number 2.3987 has four decimals. Or we can talk about adding decimals or adding decimal numbers. |
4. Name the place value that has been underlined in the number.
| a. | 345.9 | b. | 345.9 | c. | 2,305 | h. | 10.1 |
5. Write the following numbers in the normal form. Be careful!
The biggest place values are not necessarily first.
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6. Break down the following numbers. Then read the numbers in
two different forms.
| a. | 456.4 = 400 + 50 + 6 + |
4 |
f. | 203.0 | |||
| b | 0.3 | g. | 9090.3 | ||||
| e. | 600.3 | j. | 30.5 |
7. Match each expression from the first column with one from the second.
[available in the ebook]
Next lesson: Add decimal numbers with tenths
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The ideas in this decimals lesson are taken from Math Mammoth Decimals 1 book ($4.00 download). Only a few examples of each problem type are shown. |
The fast, FUN, and easy way to learn multiplication. Learn the upper times tales in two sittings using mnemonic stories.
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