the value of a digit in a decimal is determined by its ___________ or place. for example, given the...
TRANSCRIPT
NOTES 3.3 – EXPLORING DECIMALS
The value of a digit in a decimal is determined by its ___________ or place.
For example, given the decimal 0.35, the 3 is in the _________ place and the 5 is in the ________________ place.
PLACE VALUE
POSITION
TENTHSHUNDREDTHS
1, 2 3 4 . 5 6 7 8
THOUSANDS(1,000)
HUNDREDS(100)
TENS(10)
ONES(1)
TENTHS(0.1)
HUNDREDTHS(0.01)
THOUSANDTHS(0.001)
TEN-THOUSANDTHS
(0.0001)
What is this number?
_____ thousand, _____ hundred ______________ AND ____ thousand, _____ hundred ________________ ten thousandthsONE TWO THIRTY-FOUR FIVE
SIX SEVENTY-EIGHT
A ________________ is a number written with both a whole number and a fraction.
Useful Information:
To enter mixed numbers on a calculator:
Type in the whole number + ( fraction )
3 ½ would be entered as 3 + (1/2)
5.45 455
100 9
520
MORE FRACTIONS
MIXED NUMBER
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
hundred-thousandth
b) twenty-two and two
thousand five hundred
ten-thousandths
22.25001
224
11,000
100,0001,000.00001
A decimal is called a terminating decimal if the decimal number terminates, or _______.
A decimal is called a repeating decimal if the decimal number does not terminate. It repeats a ___________.
TERMINATING AND REPEATING DECIMALS
ENDS
PATTERNS
Bar Notation: A bar indicates what number(s) in the decimals will repeat:
Rewrite the repeating decimals using bar notation
A.) 56.11111… B.) -4.356356356…
0.66666...
56.1 4.356
0.6
Examples:
Use division to determine whether each of the following fractions terminate or repeat.
A.) B.)
C.) D.)
4
51
3
5
841
333
0.8 0.3333...
TERMINATES REPEATING
0.625 0.123123...
TERMINATES REPEATING
0.3
0.123
1.) __________ each decimal with the _______ number of decimal places
2) _______ up the decimal points
3) Write the numerals in ________.
4) Change the decimals to the ___________ form.
COMPARING DECIMAL NUMERALS
REWRITE SAME
LINE
ORDER
ORIGINAL
Order the decimals from least to greatest
A.) 5.32, 5.2, 4.97, 5.037, 5.3
Most number of decimal places?
B.) -7.11, -7.011, -7.105, -7.01, -7.1
Most number of decimal places?
35.320 5.200 4.970 5.037 5.300
______________________5.325.2,4.97, 5.037, 5.3,
______________________
37.110 7.011 7.105 7.010 7.100
7.11, 7.011,7.105, 7.017.1,
Write each decimal as a fraction or mixed number in lowest terms
Fraction Lowest Terms
a) .23
b) 4.015
154
1000
23
100 23
100
34
200
c) 45 .45
d) 81.225
22581
1000
45
10045
9
2045
981
40
Order the numbers from least to greatest;
a) b).
7.3 7.3
37 7.375
87.045 7.045
57 7.83
61
7 7.33
3 5 17.3, 7 , 7.045, 7 , 7
8 6 3
1 3 57.045, 7.3, 7 , 7 , 7
3 8 6
7.300
7.375
7.045
7.833
7.333
2 3 10.6, , 0.75, ,
3 8 3
0.6 0.6
20.6
30.75 0.75
30.375
81
0.33
0.600
0.666
0.750
0.375
0.333
2 3 10.75, , 0.6, ,
3 8 3
HOMEWORK: P. 146 #6-35, 36-47, 54-69