NOTES 3.3 – EXPLORING
DECIMALS
PLACE VALUE
The value of a digit in a decimal is determined
by its ___________
POSITION or place.
For example, given the decimal 0.35, the 3 is in
the _________
TENTHS place and the 5 is in the
________________
HUNDREDTHS place.
1
TENS
THOUSANDTHS
TENTHS
(10)
(0.001)
(0.1)
HUNDREDS
ONES
(100)
HUNDREDTHS
TEN(1)
(0.01)
THOUSANDTHS
THOUSANDS
(0.0001)
(1,000)
1, 2 3 4 . 5 6 7 8
What is this number?
_____
____
THIRTY-FOUR AND FIVE
ONE thousand, _____
TWO hundred ______________
thousand, _____
SIX hundred ________________
SEVENTY-EIGHT ten thousandths
MORE FRACTIONS
A ________________
MIXED NUMBER is a number written with both
a whole number and a fraction.
45
9
5.45  5  5
100
20
Useful Information:
To enter mixed numbers on a calculator:
Type in the whole number + ( fraction )
3 ½ would be entered as 3 + (1/2)
2
Write the following numbers as a decimal and a mixed
number with the fraction in lowest terms.
Decimal
Mixed Number
a) one thousand and one
1,000.00001
hundred-thousandth
b) twenty-two and two
thousand five hundred
ten-thousandths
1,000
22.2500
1
100,000
22
1
4
TERMINATING AND REPEATING
DECIMALS
A decimal is called a terminating decimal if
the decimal number terminates, or _______.
ENDS
A decimal is called a repeating decimal if the
decimal number does not terminate. It repeats
a ___________.
PATTERNS
3
Bar Notation: A bar indicates what number(s) in the
decimals will repeat:
0.66666...  0.6
Rewrite the repeating decimals using bar notation
A.) 56.11111…
B.) -4.356356356…
4.356
56.1
Examples:
Use division to determine whether each of the
following fractions terminate or repeat.
A.)
4
 0.8
5
TERMINATES
C.)
5
 0.625
8
TERMINATES
B.)
1
3
 0.3333...  0.3
REPEATING
D.) 41  0.123123...  0.123
333
REPEATING
4
COMPARING DECIMAL NUMERALS
1.) __________
SAME
REWRITE each decimal with the _______
number of decimal places
2) _______
LINE up the decimal points
3) Write the numerals in ________.
ORDER
4) Change the decimals to the ___________
ORIGINAL form.
Order the decimals from least to greatest
A.) 5.32, 5.2, 4.97, 5.037, 5.3
5.320 5.200 4.970 5.037 5.300
Most number of decimal places?
3
______________________
4.97, 5.037, 5.2, 5.3, 5.32
B.) -7.11, -7.011, -7.105, -7.01, -7.1
7.110 7.011 7.105 7.010 7.100
Most number of decimal places?
3
______________________
7.11, 7.105,7.1, 7.011,7.01
5
Write each decimal as a fraction or mixed number in
lowest terms
Fraction
Lowest Terms
23
100
a) .23
b) 4.015
c) 45 .45
d) 81.225
4
15
1000
45
81
45
100
225
1000
23
100
3
4
200
45
81
9
20
9
40
Order the numbers from least to greatest;
2
3 1
3
5
1
a) 7.3, 7 , 7.045, 7 , 7
b).0.6,  , 0.75,  , 
8
7.3  7.3
6
3
 7.300
 7.375
3
7  7.375
8
 7.045
7.045  7.045
 7.833
5
7  7.83
 7.333
6
1
7  7.3
3
1
3
5
7.045, 7.3, 7 , 7 , 7
3
8
6
3
0.6  0.6
2
  0.6
3
0.75  0.75
3
  0.375
8
1
  0.3
3
8
3
 0.600
 0.666
 0.750
 0.375
 0.333
2
3 1
0.75,  , 0.6,  , 
3
8 3
6
HOMEWORK: P. 146 #6-35, 36-47, 54-69
7