Download Lesson 30: Repeating Decimals

Bell Work:
If 479 stocks advanced in price
and 326 declined in price, then
what was the approximate ratio of
advancers to decliners?
Answer:
5 to 3
Recall that to express a ratio as a
decimal number, we perform the
division indicated. For example, to
convert ¾ to a decimal number,
we divide 3 by 4.
3 ÷ 4 = 0.75
Notice that we use a decimal point
and zeros to write 3 as 3.00 so that
we could perform the division.
Some fractions convert to decimal
numbers that have repeating
digits such as 0.272727…..
Repetend*: name given to the
repeating decimals
We indicate repeating digits with
a bar over the repetend.
We write
____
0.2727272727… as 0.27.
Example:
Express the fraction as a decimal
number.
1/6
Answer:
0.166
6Γ1.000
6
40
36
40
36
__ 4
= 0.16
Example:
Express the mixed number as a
decimal number.
2 1/3
Answer:
The mixed number 2 1/3 is a
whole number plus a fraction. The
whole number is 2 and the fraction
1/3 ___
converts to 0.333…
= 2.3
Recall that converting a rational
number to a decimal form has
three possible outcomes.
1. The rational number is an
integer
2. The rational number is a
terminating decimal number
3. The rational number is a nonterminating decimal with
repeating digits
Non-terminating, non-repeating
decimal numbers are irrational and
do not result from converting a
rational number to a decimal
number.
To perform calculations with
repeating decimals we first round the
number to a suitable number of
decimal places.
Example:
Find 5/6 of $12.47.
Answer: __
5/6 = 0.83
0.83 x 12.47 = 10.3501
$10.35
Example:
Arrange in order from least to
greatest.
__
0.3, 0.3, 0.33
Answer:
0.3
=
0.300
__
0.3 = 0.333
0.33 = 0.330
__
0.3, 0.33, 0.3
Many calculators do not have
functions that enable the user to
perform arithmetic with fractions.
To convert a fraction to a decimal,
we enter the numerator, press the
÷ key, then key in the denominator
and press =.
Convert these fractions to
decimals.
10/11
11/12
17/80
Answer: ____
10/11 = 0.90
__
11/12 = 0.916
17/80 = 0.2125
To add fractions it is not necessary to
enter long repeating decimals and it
is not necessary to round the decimal
equivalents. For example, to add 5/6
and 8/3 on a calculator that has
algebraic logic (follows the order of
operations), we can use this key
stroke sequence:
5÷6+8÷3=
If your calculator has algebraic logic,
the final display should read 3.5
which equals 3 ½.
Try these operations and write the
answer in decimal form.
11/12 + 11/6
17/24 – ½
Answer:
11/12 + 11/6 = 2.75
__
17/24 – ½ = 0.2083
Many calculators do not have a
percent key. To find a given
percent of a number with a
calculator, we mentally shift the
decimal point two places to the
left before we enter the number.
Estimate 6.25% of $72.59. then use
a calculator to perform the actual
calculation and round the answer
to the nearest cent. What decimal
number did you enter for 6.25%?
Answer:
About $4.20 rounds to $4.54
Enter .0625
HW: Lesson 30 #1-30
Due Tomorrow