A) Decimal Notation and Writing Decimals in Words. ecim B) Writing Decimals in Standard Form.

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1 5.1 Introduction to Decimals A) Decimal Notation and Writing Decimals in Words. Decimals The Place Value System for Decimal Numbers Tens/ ones/ decimal point/ tenths/ hundredths/ thousandths/ ten-thousandths Hundreds Tens Ones Decimal Tenths Hundredths Thousandths Ten-thousandths Reading and Writing Decimal Numbers a) b) c) d) twenty and four thousandths e) six and two hundred forty-seven thousandths B) Writing Decimals in Standard Form. Five hundred and ninety-six hundredths. Thirty-nine and forty-two thousandths.

2 C) Writing Decimals as Fractions. a) Write as a fraction. b) Write as a mixed number. Write each decimal as a fraction or mixed number. Write your answer in simplest form. c) 0.12 d)64.8 c) D) Comparing Decimals. Insert a > or < to complete each statement. a) b) c) d) Graph -1.1, -0.6, 0.8, and 1.9 E) Rounding Decimals. Round to the nearest i) tenth, ii) thousandth a) b) c)

3 5.2 Adding and Subtracting Decimals A) Adding or Subtracting Decimals Adding Decimals a) Subtracting Decimals a) b) Adding and Subtracting signed Decimals a) (-2.32) b) c) d) (-4.4) e) -4.9 ( ) [2.4 ( )] (-2.4)

4 B) Estimating When Adding or Subtracting Decimals a) b) C) Using Decimals as Replacement Values Evaluate y z for y = 11.6 and z = 10.8 D) Simplify Expressions Containing Decimals. -4.3y y E) Solving Problems by Adding or Subtracting Decimals. a) In 1995, the average credit-card late fee was $ By 2005, the average fee had increased to $ By how much did the average credit-card- late fee increase from 1995 to 2005? (Source: Money magazine)

5 b) Use the chart to answer the following questions. The World's Top Chocolate-Consuming Countries How much chocolate does the average German consume than the average citizen of the United Kingdom? How much more is the greatest chocolate consumption than the least chocolate consumption shown in the table? Pounds of Chocolate per Person per Year Source: Hershey Foods Corporation

6 5.3 Multiplying Decimals and Circumference of a Circle A) Multiplying Decimals. Multiplying Decimals 1. Multiply the decimals as if they were whole numbers. 2. Find the total number of decimal places in both factors. 3. Place the decimal point in the product so that the answer has the same number of decimal places as the total found in step 2. a) 3.2 * 5.6 b) ( )8.4 c) 5.66 * 3.3 Multiplying Decimals by Powers of 10 such as 10, 100, 1000, 10,000, Move the decimal point to the right the same number of places as there are zeros in the power of 10. a) 6.23 * 10 b) * 1000 c) 63.1 * Multiplying Decimals by Powers of 10 such as 0.1, 0.01, 0.001, , Move the decimal point to the left the same number of places as there are decimal places in the power of 10. a) 6.23 * 0.1 b) * c) * 0.001

7 Multiplying Signed Decimals a) 6.6(-5.5) b) ( )(-100) c) (-1.3) 2 d) (0.09) 2 Circumference of a Circle Circumference is the distance around a circle, this distance depends on the radius or the diameter of the circle. Find the circumference. diameter radius r = 5 in d = 22 m Circumference (c) = 2πr or πd π 3.14 Order of operations a) ( ) 2 b) Evaluate 1.3pr 3 for p = 3.14 and r = 3

8 Review: 1) 3 4(x 3) + 6(x + 3) Study Skills Builder: To complete a homework assignment, remember these four things: 1) Attempt all of it. 2) Check it. 3) Correct it. 4) If needed, ask questions about it. Take a moment and review your completed homework assignments. Answer the exercises below based on this review. 1) Approximate the fraction of your homework you have attempted. 2) Approximate the fraction of your homework you have checked (if possible). 3) If you are able to check your homework, have you corrected it when errors have been found? 4) When working homework, if you do not understand a concept, what do you personally do? 5.4 Dividing Decimals Dividing a Decimal by a Whole Number 1. Write the problem in long division form. 2. Divide as if working with whole numbers. 3. Write the decimal point in the result directly above the decimal point in the dividend. If necessary, additional zeros can be written to the right of the dividend to allow the division to proceed. a) b) 3.4 4

9 Divisors that are Decimals 1. Move the decimal point of the divisor so that it becomes a whole number. 2. Move the decimal point of the dividend the same number of places to the right. 3. Divide as if working with whole numbers. Write the decimal point in the answer directly above the decimal point in the dividend a) b) Rounding When Dividing Dividing Decimals by Powers of 10 such as 10, 100, or 1000 Move the decimal point of the dividend to the left the same number of places as there are zeros in the power of a) b) 1000 Order of Operations ( 0.63) a) 0.8 b) 2 ( 1.3) A bag of fertilizer covers 1250 square feet of lawn. Tim Parker s lawn measures 14,800 square feet. How many bags of fertilizer does he need? If he can buy only whole bags of fertilizer, how many whole bags does he need?

10 5.5 Fractions, Decimals, and Order of Operations A) Writing fractions as Decimals To write a fraction as a decimal, divide the numerator by the denominator. 3 3 a) b) c) 8 4 Repeating Decimals a) 11 4 Rounding Repeating Decimals a) 3 1 b) 7 3 c) Write in decimal form B) Compare Fractions and Decimals. Insert <, >, or = to form a true statement. a) 0.12 b) 0.54 c) 0.72 d) 0. 4

11 Write the numbers in order from smallest to largest. a), 0.302, C) Simplify Expressions Containing Decimals and Fractions Using Order of Operations a) b).. c) d) D) Solve Area Problems Containing Fractions and Decimals. h =12 inches meters 6.7 inches 3.4 meters E) Evaluate Expressions Given Decimal Replacement Values. Evaluate the expression for x = 0.4. x 2

12 5.6 Equations Containing Decimals A) Solving Equations Containing Decimals a) b) c) d) e) f)