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 Lesson 30 Repeating Decimals Recall that to express a ratio as a decimal number we perform the division indicated For example to convert ¾ to a decimal ID: 387004
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Slide1
Bell Work:
If 479 stocks advanced in price and 326 declined in price, then what was the approximate ratio of advancers to decliners?Slide2
Answer:
5 to 3Slide3
Lesson 30:
Repeating DecimalsSlide4
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 = 0.75Slide5
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…..Slide6
Repetend
*: name given to the repeating decimals
We indicate repeating digits with a bar over the
repetend
. We write 0.2727272727… as 0.27.
____Slide7
Example:
Express the fraction as a decimal number.
1/6 Slide8
Answer:
0.166
6Γ1.000
6
40
36 40 36 4= 0.16
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Example:
Express the mixed number as a decimal number.
2 1/3 Slide10
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
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Recall that converting a rational number to a decimal form has three possible outcomes.
The rational number is an integer
The rational number is a terminating decimal number
The rational number is a non-terminating decimal with repeating digitsSlide12
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. Slide13
Example:
Find 5/6 of $12.47.Slide14
Answer:
5/6 = 0.83
0.83 x 12.47 = 10.3501
$10.35
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Example:
Arrange in order from least to greatest.
0.3, 0.3, 0.33
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Answer:
0.3 = 0.300
0.3 = 0.333
0.33 = 0.330
0.3, 0.33, 0.3
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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 =. Slide18
Convert these fractions to decimals.
10/11
11/12
17/80Slide19
Answer:
10/11 = 0.90
11/12 = 0.916
17/80 = 0.2125
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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. Slide21
Try these operations and write the answer in decimal form.
11/12 + 11/6 17/24 – ½ Slide22
Answer:
11/12 + 11/6 = 2.75
17/24 – ½ = 0.2083
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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. Slide24
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%?Slide25
Answer:
About $4.20 rounds to $4.54
Enter .0625Slide26
HW: Lesson 30 #1-30
Due Tomorrow