KU122 Unit 3 Seminar Decimal Notation

1. KU122 Unit 3 SeminarDecimal Notation • KU122-20 Introduction to Math Skills and Strategies • Seminars: Wednesdays at 8:00 PM ET • Instructor: Tammy Mata • Email: tmata@kaplan.edu • Office Hours: By appointment • AIM: tammymataku • The seminar will begin at the top of the hour. • Audio will be available when the seminar begins.

2. DECIMAL NOTATION • Decimal Notation is a fractional value with a denominator of the power 10 AND is expressed with a decimal point: .2 is “decimal point 2” and means the same as 2/10. • Decimal Notation to indicate cents with money is extended to a fractional value with a denominator of the power 100 AND is expressed with a decimal point: $3.52 is “three dollars AND fifty-two cents” and means three whole dollars and 52/100 (or 52 cents out of 100 cents because 100 cents makes one dollar). • Decimal Values have place values that extend to the right past the decimal point—see Place-Value Chart on page 174. Therefore, .3385 is the same as 3385/10,000. • Use the word “AND” where the decimal point is when discussing decimal notation. • Additional terms to know apply to labels for division statement: divisor, dividend, and quotient: 16 ÷ 2 = 8 Divisor Dividend Quotient

3. Decimal Notation 3.1 – Converting Between Decimal Notation and Fraction Notation (pages 176 and 177). 3.2 – Addition and Subtraction of Decimal Notation. Easier to work vertically (up and down) and ALWAYS line up the decimal points (pages 184 – 186). 3.2 – Solving for Equations (page 187) may be needed when translating an application problem to an equation (very important). 3.3 – Multiplying Decimal Notation (pages 192 and 193) requires straight multiplication while ignoring the decimal points to treat the factors as whole numbers and then placing the decimal point in the product based on the sum of the number of places counting from the right: 85.4 x 6.2 = 529.48 (not 5294.8) Factor Factor Product .4 and .2 total two place values so the product must have two place values

4. Decimal Notation 3.4 – Dividing Decimal Notation has several methods based on whether the divisor is a whole number or decimal notation. (a) Whole number divisors are treated the same as regular division of whole number. When working the problem, work vertically and place the decimal point within the answer right above the decimal point in the dividend (page 200). (b) Decimal notation divisors require that the divisor be converted into a whole number by moving the decimal to the right AND that the dividend’s decimal be moved the same number of place values to the right—both the divisor and the dividend must have their decimal points moved the same place values (page 202). 3.4 – The same rules for order of operations used for whole numbers and fraction notations apply: Parenthesis, Exponents, Multiplication/Division, Addition/Subtraction Memory Tip: Please Excuse My Dear Aunt Sally When working multiplication/division, work from left to right, doing whichever one comes first. When working addition/subtraction, work from left to right, doing whichever one comes first.

5. Decimal Notation 3.5 – To convert from fraction notation to decimal notation (page 211) divide the numerator by the denominator. 3.5 – Calculations with both fraction notation and decimal notation require that the notations be converted to match; in other words, they need to all be fraction notations or all be decimal notations (page 215). 3.6 – Estimating decimal notation requires understand the place values. For example, rounding .279 to its nearest tenth is .3 but rounding .256 to its nearest hundredth is .28 (pages 220). Memorize the place-value chart on page 174. 3.7 – Application (word problems) are many. Remember the five steps for application problems: familiarize, translate, solve, check, state full answer with appropriate units of measurement as appropriate.

6. Decimal Notation Project Tips • Do NOT rely on the calculator for the answer. • Show the work! • Show the work so that it is easy to comprehend and read—formatting counts (as well as spelling and correct use of symbols). • Have the KU Writing Center review your project’s work and answers before submitting for a grade. • Follow the specific instructions at the top of the project and within each item, such as use decimal points only in original problems with decimal points, simplify answers to lowest terms, and state answers to application problems with correct units of measurements and/or references.

7. Unit 3 Practice Problems NOTE: You must know how to add, multiply, divide and simplify fraction notations from Unit 2. See page 154, number 36!!! 3.5 - Converting fraction notations to decimal notations, page 211. See examples. Practice numbers 1, 3, 5, and 6. 3.7 – Application problem for gas mileage, example 7, page 231. Answer these two questions: (1) How many miles were driven? (2) How many miles per gallon (mpg) of gasoline did the automobile get? Practice number 7 in margin exercise on page 231. Solve for questions 1 and 2 above. REMINDERS: • Show work—do not just tap into the calculator and write only the answer! • Write answers in appropriate format—fraction notations for fraction notation problems, decimal notations for decimal notation problems, and conversion of notations as required. • State answers with appropriate wording and units of measurement as needed. • Spelling, formatting, and use of correct symbols and terms count!