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

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 number, we divide 3 by 4. 3 ÷ 4 = 0.75

Notice that we use a decimal point and zeros to write 3 as 3 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 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 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. The rational number is an integer The rational number is a terminating decimal number The rational number is a non-terminating 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

Answer: 11/12 + 11/6 = 2.75 17/24 – ½ = 0.2083 __

Many calculators do not have a percent key 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