This is a complete lesson with instruction and varied exercises, explaining how the place value system works with decimals that have one decimal digit, and how to write such decimals in expanded form. It is meant for fourth grade.
Place value and expanded form
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.
Above, we have written the number 6,702 in expanded form, or as a SUM of its different parts according to 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
also called 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.
1. These numbers are written in expanded form. Write them the normal way.
a. 7 + 40 + 300
d.
9000 + 5 + 30
b. 8000 + 70 + 5
e.
9 + 4000
c. 60 + 400 + 2
f.
200 + 2 + 50
2. Write the following numbers the normal way.
a. 7 × 1
f.
6 × 100 + 5 × 10
b. 8 × 10 + 7 × 1
g.
7 × 1000
+ 2 × 100 + 2 × 10 + 8 × 1
c. 6 × 10 + 0 × 1
h.
4 × 1000 + 6 × 10
d. 8 × 10
i.
6 × 1000 + 2 × 1
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 the next bigger place
value be after
thousands?
What would the next smaller place
value be 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!!!
In expanded form:
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
12.3
10 + 2 +
3
10
twelve and three tenths
OR
twelve point three
45.9
forty-five and nine tenths
OR
382.1
300 + 80 + 2 +
1
10
607.6
1,330.3
10,560.2
Note: the word decimal can mean TWO things:
1. decimal = a 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
d. 30.5
e. 6.5
f. 2,305
g. 2,005.4
h. 10.1
5. The the following numbers are written in expanded form. Write them in the normal form.
Note: the parts are not listed in order.
a.
4
10
b.
2 +
5
10
c.
90 +
9
10
d.
50 +
1
10
+ 4
e.
6 + 80 +
7
10
f.
2
10
+ 70
g.
500 + 10 +
7
10
h.
600 + 8 +
9
10
+ 6000
i.
30 + 9000 + 5 +
3
10
j.
200 + 2000
+ 90 +
8
10
6. Write the following numbers in expanded form. 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
c.
304.5
h.
398.9
d.
4,676.6
i.
0.8
e.
600.3
j.
30.5
7. Match each expression
from the first column
with one from the second.
A self-teaching worktext for 4th grade that gives a solid foundation for decimals. It covers tenths and hundredths, comparing decimals, adding and subtracting decimals both mentally and in columns, multiplying decimals by whole numbers, rounding, estimating, and money problems.
Download ($3.50). Also available as a printed copy.