1. Math 20 Pre Algebra Decimal Fractions and Scientific Notation ©sdmix/123RF.COM

2. Decimal Fractions and Scientific Notation 2 Developed By TimO'Brien SWBAT 1. Read and write decimal fractions. 2. Add and subtract signed decimal fractions. 3. Read and write scientific notation for whole numbers. 4. Read and write scientific notation for decimal fractions.

3. 3 Internet Connection Developed By Tim O'Brien

4. Decimal Fractions and Scientific Notation Decimal Fractions 4 By 980 Abu'l Hasan Ahmad ibn Ibrahim Al-Uqlidisi, most probably from Damascus, Syria, (see map ), had introduced the decimal fractions. A decimal fraction is a fraction that has a power of 10 for its denominator. The brilliant idea of Abu'l Hasan Ahmad was to write these fractions by extending the decimal place value system. No longer did we need to write denominators for fractions; we could simply put numerators in their correct decimal places. Developed By TimO'Brien

5. 5 Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones Tenths Hundredths Thousandths Ten thousandths Hundred thousandths Millionths 10 6, 10 5 10 4 10 3, 10 2 10 1 10 0. 10 -1 10 -2 10 -3 10 -4 10 -5 10 -6 Place Value Chart Developed By TimO'Brien Using the table below, we can see Abu’l Hasan Ahmads idea. Instead of writing or saying ½, we write 0.5 and say “five tenths.” Instead of, we write 0.007 and We say “seven thousandths.”

6. Decimal Fractions and Scientific Notation Decimal Fractions 6 RULE: Read and say decimal fractions in English, using these three steps in order: 1.If there is an integer before the decimal point, name the integer part. Next read “and” for the decimal point. Otherwise skip this step. 2.For the decimal fraction, ignore zeros and say the number after the decimal as if it were a second integer. 3.Say the decimal place value for the last digit given after the decimal point. Developed By TimO'Brien

7. a) 0.006 is read, “six thousandths.” A typical hourly dosage of morphine depends upon the patient’s age. Write how to say the decimal fraction using words. a.A 16-year old would receive 0.006 grams per hour b.A 40-year old would receive 0.0025 grams per hour. c. A 25-year old would receive 0.003125 grams per hour. b) 0.0025 is read, “twenty-five ten-thousandths.” 7 c) 0.003125 is read “ three thousand one hundred twenty-five millionths.” Developed By TimO'Brien SOLUTION

8. a) 93.530 is read, “ninety-three and five hundred thirty thousandths.” Write how to say the decimal fraction using words. a.The new Ford Scorpion, sold now in the United Kingdom, has a cylinder core diameter of 93.530 mm. b.A certain extension cord has 1.277 ohms of resistance. b) 1.277 is read, “one and two hundred seventy- seven thousandths.” 8 Developed By TimO'Brien

9. Decimal Fractions and Scientific Notation Add and Subtract Signed Decimals 9 From the very beginning of recorded civilization, people have paid taxes and tithes for the protective, organizational, and civilizing services that governments and religious orders provide. The words decimal and tithe both have their roots in paying money in tenths. In our democratic republic we have the right to vote, or have our representatives vote, on our own taxation. The property taxes we pay are actually a sum of several assessed taxes, and these amounts are reported using decimals. Developed By TimO'Brien

10. SOLUTION 1.Estimate by rounding to the nearest whole number: 1+6+6+0+0+0+1=$14 per 1,000 of assessed value. Chesney lives in Grants Pass, and her property taxes were assessed to pay for the services listed in the table on the right. What was the total property tax rate in Grants Pass for 2007? 10 2.The total property tax rate in Grants Pass for 2007 was $14.2611 per $1000 of assessed value. Developed By TimO'Brien

11. SOLUTION 11 Subtract the following. a. -25.4 - 983.2 b.-3.08 + 0.905 - 3.42 a) -25.4 - 983.2 b) -3.08 + 0.905 -3.42 = -3.08 + 0.905 + (-3.42) = -5.595 = -25.4 + (-983.2) = -1008.6 Developed By TimO'Brien

12. 12 Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones Tenths Hundredths Thousandths Ten thousandths Hundred thousandths Millionths 10 6, 10 5 10 4 10 3, 10 2 10 1 10 0. 10 -1 10 -2 10 -3 10 -4 10 -5 10 -6 Place Value Chart Developed By TimO'Brien

13. Decimal Fractions and Scientific Notation Writing a Number in Scientific Notation 13 Move the decimal point to the right of the first nonzero digit. Count the number of places the decimal point was moved. The number of places the decimal was moved is the exponent on 10. The exponent of 10 is positive if the original number is greater than 1; the exponent is negative if the original number is less than 1. Developed By TimO'Brien

14. SOLUTION 239,000 = 2.39 x10 5 92,900,000 = 9.29 x10 7 a) Write using scientific notation. a.The average distance from the Earth to the sun: 92,900,000 miles. b.The average distance from the Earth to the moon: 239,000 miles c.The amount of caffeine in a cup of hot chocolate or cocoa is 0.005 grams. d.The amount of caffeine in a brewed cup of coffee is 0.135 grams. b) 14 miles 0.005 = 5.0 x10 -3 c) grams 0.135 = 1.35 x10 -1 d) grams Developed By TimO'Brien

15. SOLUTION 0.000000002 = 2.0 x10 -9 6,787,000,000 = 6.787 x10 9 a) Write using scientific notation. a.In August, 2009 the approximate population of the world was 6,787,000,000. b.The length of the Ebola virus is 0.000 000 002 meters b) 15 people meters Developed By TimO'Brien

16. SOLUTION 1.8 x10 11 2.5 x10 7 a) Write using Standard notation (decimal notation). a.In one single day, over 2.5 x 10 7 dollars are spent on weight loss programs in the U.S. b.About 1.8 x 10 11 e-mails will be sent worldwide today. c.Airborne pollutants below 2.5 x 10 -9 meters in diameter are called PM. d.The width of your hair is based on your genetics. The widest human hair is about 1.8 x 10 -7 meters wide. b) 16 = 25,000,000 dollars = 180,000,000,000 e-mails 2.5 x10 -9 c) =.0000000025 meters 1.8 x10 -7 d) =.00000018 meters Developed By TimO'Brien

17. SOLUTION 1.45 x10 -8 2.86 x10 9 a) Write using Standard notation (decimal notation). a)In one day over 2.86 x 10 9 kilowatt hours (kWh) of solar energy strike the Earth. b)The width of your hair is based on your genetics. The widest human hair is about 1.45 x 10 -8 meters wide. b) 17 = 2,860,000,000 kwh =.0000000145 meters Developed By TimO'Brien