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starMay 2013

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Math Mammoth Decimals 1 book cover 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.

Tenths - place value
Free decimals lesson plan from HomeschoolMath.net

The base 10 number system - place value

6  , 7 0 2
thou-
sands
hund-
reds
tens ones
6,702  =  6 thousands and 7 hundreds and 0 tens and 2 ones
=  6 × 1000 + 7 × 100 + 0 × 10 + 2 × 1 
=  6000  +  700  +  2.

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.
6 , 7 0 2
thou-
sands
hund-
reds
tens ones
_____ _______________ What is the rule (or relationship) between the different place values?

What would be the next bigger place value after thousands?  

What would be the next smaller place value after ones?

1000 (thousands)
100 (hundreds)
10 (tens)
1 (ones)
 _____  _______________

Tenths

4 2 . 9
tens ones tenths
The digit 9 comes right after the decimal point.  Nine is in the tenths place.
It means 42.9 has 9 tenths or tenth parts.  We are back to fractions!!!
 
42.9  = 4 tens and 2 ones and 9 tenths  

 = 4 × 10 + 2 × 1 + 9 ×  1

10
    = 40 + 2 +   9

10
Read: forty-two and nine tenths
OR
forty-two point nine

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.

6 , 7 0 5 . 7
thou-
sands
hund-
reds
tens ones tenths
This number has a decimal point.  It also has a comma separating
the thousands from the other digits (for easier reading).
6,705.7  = 6 thousands and 7 hundreds and 0 tens and 5 ones and 7 tenths
 =  6 × 1000 + 7 × 100 + 0 × 10 + 5 × 1 + 7 × 1

10
    = 6000 + 700 + 5 +   7

10
Read: six thousand seven hundred five and seven tenths
OR  six thousand seven hundred five point seven

If there is no whole number part, some people omit the zero and write 0.7 as .7 etc. 



3.  Fill in the missing parts and read aloud.

Number    Broken down    Read
.5 = 0.5

5

10

five tenths OR  point five/zero point five
1.8
1 + 

8

10

one and eight tenths  OR  one point eight
607.6        
1,330.3        

Note: the word decimal can mean TWO things:
1) decimal = decimal number = a number that has digits after the decimal point
2) decimal = a digit after the decimal point.

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.

a.     4

10
i. seven and a half
b 2 +  5

10
j. 30 + 9000 + 5 +  3

10
c 90 +  9

10
k. 200 + 2000 + 90 +  8

10
d. 50 +  1

10
 + 4 
l. 9 +  0

10
+ 30 + 4000

 
6.  Break down the following numbers.  Then read the numbers in two different forms.

a. 456.4 = 400 + 50 + 6 +  

4

10

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


Math Mammoth Decimals 1 book cover 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.

Practice makes perfect. Practice math at IXL.com

Free math worksheets and practice - Adapted Mind

Practice makes perfect. Practice math at IXL.com


New! Times Tales is now on DVD!

The fast, FUN, and easy way to learn multiplication. Learn the upper times tales in two sittings using mnemonic stories.
 
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