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Three Decimal Digits - Thousandths

This is a complete lesson with instruction and exercises about decimals with three decimal digits: writing them as fractions, place value & expanded form, and decimals on a number line. It is meant for 5th grade.

In the video below, I explain decimals with three decimal digits—or thousandths—using fractions and a number line. Then I show examples of converting fractions to decimals and vice versa.



This square illustrates one whole. It is divided into a hundred parts
or hundredths. The top left square is divided into ten new parts.
Those are thousandths.

The 6 shaded parts represent  6

1000
, or 0.006 (six thousandths).

The third decimal digit from the decimal point is the thousandths digit.
For example, 0.008 is eight thousandths.

Read the whole set of three decimal digits as a number, and say “thousandths.”

0.391 is read “391 thousandths.” As a fraction, it is  391

1000
.
0.047 is read “47 thousandths.” As a fraction, it is  47

1000
.
From the place value chart, we can see that the number
0.825 has 8 tenths, 2 hundredths, and 5 thousandths.

Writing 0.825 as a sum of those “parts” is called
writing it in expanded form.

 
O   t h th
0 . 8 2 5

 

0.825 = 8 × 1

10
 +  2 × 1

100
 +  5 × 1

1000

While 0.825 is the sum of 8/10, 2/100, and 5/1000, it is also 825/1000 (825 thousandths).
How can that be?

Because 8/10 is equal to 800/1000 and 2/100 is equal to 20/1000. So, when you add 8/10, 2/100, and 5/1000, you will get 825/1000.

1. Write the numbers in their expanded form. Write them also as fractions. The first one is done for you.

a.

O   t h th
0 . 9 0 6

=

906

1000

 

    = 9 × 1

10
 +  0 × 1

100
 +  6 × 1

1000

b.

O   t h th
0 . 2 4 4

=

 

    =        × 1

10
 +        × 1

100
 +        × 1

1000

c.

O   t h th
0 . 6 5 5

=

 

    =       × 1

10
+

d.

O   t h th
0 . 1 8  

=

 

    =

e.

O   t h th
0 . 8 0 2

=

 

    =       × 1

10
+

f.

O   t h th
0 . 7 1 1

=

 

    =

2. These numbers have also hundreds, tens, and ones. Write the numbers in the expanded form. Follow
    the example.

a.

T O   t h th
6 3 . 9 2 6
 =  6 × 10  +  3 × 1  +  9 ×  1

10
  +  2 × 1

100
  +  6 × 1

1000

b.

T O   t h th
2 4 . 7 8 8
 =        × 10  +        × 1  +        ×  1

10
  +        × 1

100
  +        × 1

1000

c.

T O   t h th
  4 . 9 0 2
 =        × 1  + 

d.

T O   t h th
7 4 . 7 2  
 = 

e.

H T O   t h th
1 5 1 . 9    
 =        × 100  + 

f.

H T O   t h th
7 6 5 . 2 4 4
 =        × 100  + 

3. Write the decimals in the place value charts, and as fractions.

a.  seven thousandths

 
O   t h th
  .      
=

b.  8 tenths and 2 thousandths

 
O   t h th
  .      
=

c.  3 and 371 thousandths

 
O   t h th
  .      
=

d.  39 thousandths

 
O   t h th
  .      
=

e.  1 and 41 hundredths

 
O   t h th
  .      
=

f.  7 and 4 thousandths

 
O   t h th
  .      
=

4. Write in expanded form.

    a. 0.95  =

    b. 1.405  =

    c. 244.781 =

    d. 65.05  =

    e. 20.214  =



This number line has tick marks at every hundredth. For thousandths, we would need to divide each such interval into ten new intervals. Imagine that in between each two tick marks there are nine little lines. Those would represent thousandths.

The numbers 0.052, 0.145, 0.228, and 0.304 are marked on the number line. Can you find them?

Reminder: You can “tag” zeros on the end of a decimal number, and its value will not change:

O   t h th
0 . 7    
0 . 7 0  
0 . 7 0 0
 
0.7 = 0.70 = 0.700
 
Seven tenths = 70 hundredths = 700 thousandths
 
7

10
 =   70

100
 =   700

1000

5. Fill in with the kind of parts you get.

    When you divide one whole into ten equal parts, you get _________________________________. 

    When you divide one tenth into ten equal parts, you get  _________________________________. 

    When you divide one hundredth into ten equal parts, you get ______________________________. 

6. Write the decimals indicated by the arrows.

   

    a. ____________    b. ____________    c. ____________    d. ____________    e. ____________

 
7. Mark these decimals on the number line: 0.187, 0.205, 0.252, 0.301, and 0.314.

   



8. Write the fractions as decimals.

a. 

3

1000

=
b. 

12

1000

=
c. 

319

1000

=
d. 

50

1000

=
e.  4

34

1000

=
f.  2

4

1000

=
g.  3

3

100

=
h.  1

80

100

=
i.  17

3

1000

=
j. 

649

1000

=
k.  9

1

100

=
l.  50

619

1000

=

9. Write as fractions or mixed numbers.

a.  0.048  b.  3.902 c.  3.005 d.  6.7
e.  10.06 f.  12.060 g. 7.90 h.  0.429
i.  505.5 j.  4.789 k. 0.091 l.  5.42

10. What number is formed from the "parts"? Give your answer as a decimal.

a. 

3

1000

+

2

10

+

7

100

 =
b. 

8

10

+ 1 + 

9

100

 =
c. 

2

10

+ 7 +

3

1000

 =
d. 

5

10

+ 90 + 

2

100

 =

8

1000

 =
e. 

1

10

+ 7 +

8

1000

 + 10 =
f.   200 + 

8

1000

 + 5 =

11. Ten tenths makes one whole. We can write that as a multiplication: 10 × 0.1 = 1. (Note: the word
       “makes” corresponds to the equal sign, but there is no word to correspond to the multiplication sign; it is
        implied.
)
Fill in the sentences below, and write a multiplication sentence to match each one.
      Hint: The picture of the large square in the first page of this lesson can help.

  a. ________ thousandths makes a hundredth. _______ × _______ = _______
  b. ________ hundredths makes a tenth. _______ × _______ = _______
  c. ________ thousandths makes a tenth. _______ × _______ = _______
  d. ________ hundredths makes one whole. _______ × _______ = _______


12. Use the place value chart to help you, and write the decimal that is....

a.  
O   t h th
0 . 2 8 5

one tenth more than 0.285            _________

one hundredth more than 0.285    _________

one thousandth more than 0.285   _________

b.  
O   t h th
  .      

one tenth more than 0.016            _________

one hundredth more than 0.016    _________

one thousandth more than 0.016   _________

c.  
O   t h th
  .      

one tenth more than 1.07            _________

one hundredth more than 1.07    _________

one thousandth more than 1.07   _________

d.  
O   t h th
  .      

one tenth more than 0.9            _________

one hundredth more than 0.9    _________

one thousandth more than 0.9   _________

e.  
O   t h th
  .      

five tenths more than 2.316           _________

six hundredths more than 2.316     _________

two thousandths more than 2.316   _________

f.  
T O   t h th
    .      

ten more than 1.08            _________

one hundredth more than 1.08    _________

nine thousandths more than 1.08   _________

 

13. Place the numbers in the cross-number puzzle.
      The squares have been left white so as not to
      show how many digits the numbers have.
      After completing the puzzle, you can color
      or shade the squares that are left empty.
 

      Across:

      a. two and 49 thousandths

      c. two and 7 hundredths

      d. five hundredths

      e. 71 hundredths

      f. 392 thousandths

Down:

a. 2 and nine hundredths

b. 3 and 76 thousandths

c. 2 and five tenths

d. 3 thousandths

e. two tenths




This lesson is taken from my book Math Mammoth Decimals 2.

Math Mammoth Decimals 2

A self-teaching worktext for 5th-6th grade that covers the four operations with decimals up to three decimal digits, concentrating on decimal multiplication and division. The book also covers place value, comparing, rounding, addition and subtraction of decimals. There are a lot of mental math problems.

Download ($6.25). Also available as a printed copy.

=> Learn more and see the free samples!



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