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
The third decimal digit from the decimal
point is the thousandths digit. Read the whole set of three decimal digits as a number, and say “thousandths.”




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








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











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

b. 8 tenths and 2 thousandths

c. 3 and 371 thousandths


d. 39 thousandths

e. 1 and 41 hundredths

f. 7 and 4 thousandths

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:

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.














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.








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....
one tenth more than 0.285 _________ one hundredth more than 0.285 _________ one thousandth more than 0.285 _________ 
one tenth more than 0.016 _________ one hundredth more than 0.016 _________ one thousandth more than 0.016 _________ 

one tenth more than 1.07 _________ one hundredth more than 1.07 _________ one thousandth more than 1.07 _________ 
one tenth more than 0.9 _________ one hundredth more than 0.9 _________ one thousandth more than 0.9 _________ 

five tenths more than 2.316 _________ six hundredths more than 2.316 _________ two thousandths more than 2.316 _________ 
ten more than 1.08 _________ one hundredth more than 1.08 _________ nine thousandths more than 1.08 _________ 
13. Place the numbers in the crossnumber puzzle. 


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 Maria Miller's book Math Mammoth Decimals 2, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Taina Maria Miller.
Math Mammoth Decimals 2
A selfteaching worktext for 5th6th 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.