# Numbers with One Decimal Digit - Tenths

This is a complete lesson with instruction and exercises about numbers with one decimal digit (tenths), meant for fourth grade. To illustrate these decimals, we divide each whole-number interval on a number line into 10 parts. Or, we can look at fractions. The lesson includes varied exercises.

The number line between 0 and 1 is divided into ten parts. Each of these ten parts is 1/10, a tenth. Under the tick marks, you see decimal numbers such as 0.1, 0.2, 0.3, and so on.

 These are the same numbers as the fractions 1 10 , 2 10 , 3 10 , and so on.

We can write any fraction with tenths (denominator 10) using the decimal point. Simply write after the decimal point how many tenths the number has.

 0.6 means six tenths, or 6 10 .
 1.5 means 1 whole and 5 tenths, or 1 5 10 .

 Note: 1 8 is not 0.8.  Instead, 0.8 is eight tenths, or 8 10 .

The denominator is always 10!

1. Write the fractions as decimals, and vice versa.

 a. 7 10
 b.  2 4 10
 c.  10 9 10
 d.  0.9
 e.  29.3

2. Write the decimal and the fraction that the picture shows.

 a. b.  c.   3. Shade the parts to show the decimals.

 a. 0.4
 c.  1.6
 d.   2.8
 b. 0.1

 “Decimal” comes from the Latin root decem, which simply means “ten.” The number system we use is called the decimal number system, because the place value units go in tens: you have ones, tens, hundreds, thousands, and so on, each unit being 10 times the previous one. In common language, the word “decimal number” has come to mean numbers which have digits after the decimal point, such as 5.8 or 9.302. But in reality, any number within the decimal number system could be termed a decimal number, including whole numbers such as 12 or 381.

4. Write the mixed number under each decimal number. 5. Write the decimal numbers under the tick marks. 6. Make a number line from 2 till 3.5 with tick marks at every tenth. Label them with decimal numbers.

7. Compare. Write  <> , or  =  between the numbers.

a.  0.5 0.9 b.  1.3 0.3 c.  5.1 4.9
 d.  0.4 1 2
e.  16.0 16

8. Put in order from smallest to largest:

 1.2   0.9   2.6   0.1     2 1 2 2.3   3.0 1 2

9. Mark these temperatures with dots on the thermometer: 37.4°C, 36.2°C, 38.7°C, 41.8°C, 40.5°C 