Seminar 3 Welcome

Agenda Decimal/Fraction Notation Addition, Subtraction, multiplication/division with Decimals

42.3245 4 tens + 2 ones + 3 tenths + 2 hundredths + 4 thousandths + 5 ten-thousandths We read this number as “Forty-two and three thousand two hundred forty-five ten-thousandths.” The decimal point is read as “and”.

Write a word name for the number in this sentence: The top women’s time for the 50 yard freestyle is 22.62 seconds.

Write a word name for the number in this sentence: The top women’s time for the 50 yard freestyle is 22.62 seconds. Twenty-two and sixty-two hundredths

To convert from decimal to fraction notation, a) count the number of decimal places, b) move the decimal point that many places to the right, and c) write the answer over a denominator with a 1 followed by that number of zeros 4.98 2 places 4.98 Move 2 places. 2 zeros Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Write fraction notation for 0.924. Do not simplify. 0.924 = Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Write fraction notation for 0.924. Do not simplify. Solution 0.924 0.924. 3 places 3 zeros Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Example D Write 17.77 as a fraction and as a mixed numeral. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Example D Write 17.77 as a fraction and as a mixed numeral. Solution To write as a fraction: 17.77 2 zeros 2 places 17.77 To write as a mixed numeral, we rewrite the whole number part and express the rest in fraction form: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

a) count the number of zeros, and b) move the decimal point that number of places to the left. Leave off the denominator. To convert from fraction notation to decimal notation when the denominator is 10, 100, 1000 and so on, 3 zeros 8.679. Move 3 places. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Example E Write decimal notation for Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Example E Write decimal notation for Solution 1 place 1 zero Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

1. In the number 623,841, which digit tells the number of 10 thousands? Section 3.1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

1. In the number 623,841, which digit tells the number of 10 thousands? Section 3.1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Section 3.1 2. Write a word name for 8.032. a) Eight and thirty-two ten thousandths b) Eight thousand, thirty-two c) Eight and thirty-two hundredths d) Eight and thirty-two thousandths Section 3.1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Section 3.1 2. Write a word name for 8.032. a) Eight and thirty-two ten thousandths b) Eight thousand, thirty-two c) Eight and thirty-two hundredths d) Eight and thirty-two thousandths Section 3.1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Section 3.1 3. Write decimal notation for a) 4.3 b) 0.53 c) 0.053 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Section 3.1 3. Write decimal notation for a) 4.3 b) 0.53 c) 0.053 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Adding with decimal notation is similar to adding whole numbers. First we line up the decimal points so that we can add corresponding place-value digits. Add the digits from the right. If necessary, we can write extra zeros to the far right of the decimal point so that the number of places is the same. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Example A Add: 4.31 + 0.146 + 14.2 Solution Line up the decimal points and write extra zeros.4 . 3 1 0 . 1 4 6 1 4 . 2 0 0 1 8 . 6 5 6 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Example D Subtract 574 – 3.825 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Example D Subtract 574 – 3.825 Solution 5 7 4 . 0 0 0 – 3 . 8 2 5 5 7 5 7 4 . 0 0 0 – 3 . 8 2 5 3 9 9 10 5 7 . 1 7 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

1. Add: 2.15 + 13.07 + 25. a) 14.47 b) 40.22 c) 59.57 d) 47.81 Section 3.2 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

1. Add: 2.15 + 13.07 + 25. a) 14.47 b) 40.22 c) 59.57 d) 47.81 Section 3.2 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Section 3.2 4. Subtract: 70 – 8.231. a) 61.231 b) 62.769 c) 62.231 d) 61.769 Section 3.2 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Section 3.2 4. Subtract: 70 – 8.231. a) 61.231 b) 62.769 c) 62.231 d) 61.769 Section 3.2 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

To multiply using decimals: 0.8  0.43 a) Ignore the decimal points, and multiply as though both factors were whole numbers. b) Then place the decimal point in the result. The number of decimal places in the product is the sum of the number of places in the factors. (count places from the right). 2 Ignore the decimal points for now. (2 decimal places) (1 decimal place) (3 decimal places) Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

To divide by a whole number; a) place the decimal point directly above the decimal point in the dividend, and b) divide as though dividing whole numbers. Quotient Dividend Remainder Divisor Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Review for Projects A recipe for a drink calls for 1/5 quart water and ¾ quart apple juice. How much liquid is needed?

2/5 + 1/4 = 8/20 + 5/20 = 13/20 Now if the recipe is doubled?

13/20 13/20 + 13/20 = 26/20 =1 6/20= 1 3/10 Or 13/20 * 2 = 13/20 *2/1 =26/20 = 1 6/20 = 1 3/10 If the recipe is halved?

13/20 13/20 / 2 = 13/20 / 2/1 = 13/20 * ½= 13/40

Simplify and convert to decimal 2/5 x 1/6=

Simplify and convert to decimal 2/5 x 1/6= 3/30=1/10 Now change into decimal

1/10 Simplest way is to use a calculator First off, we'll interpret the fraction bar to mean "divided by." This means that 1/10 is the same as 1 divided by 10. Now, we'll just do what the fraction bar says: divide 1.0 by 10: And that's about it! 1/10 written as a decimal to 1 decimal places is 0.1.

Mileage Molly bought gasoline when the odometer read 8,678.9. After the next filling, the odometer read 8,999.9. It took 9.8 gal to fill the tank. a) How many miles did she drive? b) How many miles per gallon (mpg) did the car get?

First Step Subtraction 8,999.9 8,678.9 321 .0 She drove 321 miles Molly bought gasoline when the odometer read 8,678.9. After the next filling, the odometer read 8,999.9. It took 9.8 gal to fill the tank. First Step Subtraction 8,999.9 8,678.9 321 .0 She drove 321 miles Next divide 321 by 9.8 = 32.7 miles to the gallon.

Drew filled his truck’s gas tank and noted that the odometer read 62,957.1. After the next filling, the odometer read 63,247.5. It took 17.6 gal to fill the tank. How many miles per gallon did the truck get?

Drew filled his truck’s gas tank and noted that the odometer read 62,957.1. After the next filling, the odometer read 63,247.5. It took 17.6 gal to fill the tank. How many miles per gallon did the truck get? 63247.5 -62957.1 290. 4 290.4 / 17.6 = 16.5