* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Module 4 Worksheets Module 4A –5.1 and 5.2 5.1 Decimal Notation
Survey
Document related concepts
History of mathematics wikipedia , lookup
History of logarithms wikipedia , lookup
Location arithmetic wikipedia , lookup
Large numbers wikipedia , lookup
Principia Mathematica wikipedia , lookup
Bra–ket notation wikipedia , lookup
Abuse of notation wikipedia , lookup
Approximations of π wikipedia , lookup
Elementary mathematics wikipedia , lookup
History of mathematical notation wikipedia , lookup
Musical notation wikipedia , lookup
Transcript
Module 4 Worksheets Module 4A –5.1 and 5.2 5.1 Decimal Notation Objective A –Given decimal notation, write a word name, and write a word name for an amount of money Label the place value in the number. 4 3 8 We can continue to write place value to the right of the one’s place after a decimal point. Label the place values that occur after the decimal point: 438._________ ___________ ___________ 438.752 is written in decimal notation. How do we read this number? How do we write a word name for decimal notation? a) b) c) Write a word name for the number in the sentence: The world record in the men’s 800 meter run is 1.6852 min, held by Wilson Kipketer of Denmark. Write in words, as on a check: $524.95 Objective B- Convert between fraction notation and decimal notation. 3.57 stands for what? To convert from decimal to fraction notation: a) b) c) Write 0.0109 as a fraction. Write -2.6073 as a fraction and as a mixed number. Fraction: Mixed number: To convert from fraction notation to decimal notation when the denominators are 10, 100, 1000, and so on: a) b) Convert 9 to decimal notation. 100 Write decimal notation for 7 13 1000 Objective C – Given a pair of numbers in decimal notation, tell which is larger. We can graph numbers on a number line. Graph 1.09 and 1.3 on the number line below. Which number is larger? 1.3 or 1.09 1.3 ____ 1.09 How do we compare two positive numbers written in decimal notation? Which number is larger? 0.403 or 0.410 Graph -0.15 and -0.187. Draw the number line below. Which one is larger? -0.15_______-0.187 How do we compare two negative numbers in decimal notation? Which number is larger? -3.8 or -3.82 -3.8 ______ -3.82 Objective D – Round decimal notation to the nearest tenth, hundredth, thousandths, or ten, hundred, thousand To round to a certain place: a) b) c) Round 72.3846 to the nearest hundredth. Round -0.372 to the nearest tenth. 5.2 Addition and Subtraction of Decimals Objective A – Add using decimal notation What do we do when we add decimals? Why do we line up decimals? Add: 56.314+17.78 Add: 0.34+3.5+0.127+768 Objective B – Subtract using decimal notation How do we subtract decimals? Subtract: 56.314-17.78 How do we check subtraction? Subtract: 2 – 1.0908 Objective C – Add and Subtract Negative Decimals To add a negative number and a positive number: a) b) c) Add: 14.301 + (-17.82) To add two negative numbers: a) b) Add: -2.9 + (-4.3) Subtract: -4.9 – 5.392 Subtract: -7.9 - (-8.5) STOP THE VIDEO AT THIS POINT! DO NOT CONTINUE TO THE NEXT OBJECTIVE. TIME FOR 5.1 AND 5.2 HOMEWORK. Module 4B - Multiplication of Decimals Obj. 1 Multiply using decimal notation Multiply 2.3 × 1.12 by converting the decimals to fractions. What conclusion can be drawn about the number of decimal places? Multiply 0.02 × 3.412 by converting to fractions. Does the conclusion about the number of decimal places above hold true? To multiply using decimals, use the following steps: a) b) Multiply 6.3 X 84.7 .0032 X 2148 : 749(-0.43) To multiply any number by a tenth, hundredth, thousandth (or so on), use the following steps: a) b) Multiply by moving decimals and inserting zeros as necessary. 0.1 X 79.81 0.01 X 243.7 .001 X (-52.8) .0001 X 61.5 To multiply any number by a power of ten, follow the following steps: a) b) Multiply by moving decimals and inserting zeros as necessary. 10 X 42.63 -7.8 X 100 1000 X (-2.4167) 10,000 X 9.51 Obj. 2 Convert between dollars and cents and convert words names 1) How many decimals places do you move for each of the following? a) hundred b) thousand c) million d) billion e) trillion 2) How do you write 67.3 million in standard notation? 3) How do you convert from dollars to cents? 4) Convert to cents. $189.64 $0.66 5) How do you convert from cents to dollars? 6) Convert to dollars. 783₵ 4205₵ STOP THE VIDEO AT THIS POINT!!! DO NOT CONTINUE TO THE NEXT OBJECTIVE. Go to homework 5.3. Module 4C - Division of Decimals Obj. 1 Divide using decimal notation 1) The number of decimal places in the quotient is always equal to the number of decimal places in the ____________? To divide by a whole number, follow the following steps: a) b) 2) Divide 3) a) If you don’t have a decimal point you must add it at the __________________ of the number. b) Divide: 5 82 4) To divide by a non-whole number, follow the following steps: a) b) 5) 6) What is quick method for dividing by a power of 10? a) b) 7) Divide: 213.4567 100 STOP THE VIDEO AND ANSWER THE FOLLOWING QUESTION. CONTINUE WITH THE VIDEO AFTER THE QUESTION IS ANSWERED: 8) How many places and in what direction would you move the decimal when dividing by 10000? 9) To divide by a tenth, hundred, or thousand, we follow the same steps as above except instead we move the decimal which direction? 10) Divide: 1.0237 0.001 STOP THE VIDEO AT THIS POINT!!!! DO NOT GO ON TO THE NEXT OBJECTIVE Go to homework 5.4. Module 4D 5.5, 6.2, 6.3 5.5 More with Fractions and Decimal Notation Objective A – Convert Fractions to Decimal You can use ______________________________ to convert from fraction notation to decimal notation. One way to explain how to properly set up your division problems has been described as using the dumptruck. Think of a dump truck. The truck is on the bottom and the load is on the top (just like the denominator is on the bottom of a fraction and the numerator is on the top. Now think of the long division symbol as the hole being filled by the dumptruck. The truck stays outside the hole and the load falls in the hole. The fraction 7 can also be written as : 8 Using the long division symbol, find the decimal equivalent to 7 . 8 What is a terminating decimal? What is a repeating decimal? Find the decimal equivalent for 4 . What is strange about the result? 11 Where does the bar go in a repeating decimal? Obj. 2 Round decimal notation Find the decimal equivalent for 7 . 12 Write the answer in a short-hand way (with the appropriate bar): Write the answer without using a bar. Why might we want to do this when rounding? 1) Round to the nearest tenth 2) Round to the nearest hundredth 3) Round to the nearest thousandth Obj. 3 Converting fractions to decimal We can use _______________ ___________________ to convert from fraction notation to decimal notation. Convert directly to decimal without dividing 7 4 = For what denominators are you able to convert without explicitly dividing? Obj. 4 Simplify an expression with both fraction and decimal notation Calculate 47 79.95) 9 Why is it not a good idea to convert the fraction to a decimal in the above problem? 6.2 Percent Notation Obj. 1 Three kinds of notation for percent What are the three kinds of notation for percent? Write three kinds of notation for 27.5% Obj. 2 Convert between decimal and percent notation Find decimal notation for 45.6% What effect does multiplying by .01 have on the number being multiplied? To convert from percent notation to decimal notation use the following steps: a) b) Find decimal notation for .18% Find decimal notation for 700% When a decimal is not shown where do you put it? Find percent notation for .03 To convert from decimal notation to percent notation use the following steps: a) b) Find percent notation for .017 6.3 Percent and Fraction Notation Obj. 1 Convert fraction notation to percent notation Can you go always go straight from fraction notation to percent notation? __________ What do you need to do first? ______________________________________________ Convert 13 to percent notation. 16 When you convert Convert 2 to a decimal, what kind of decimal is it? 3 2 to percent notation. 3 Why is it quicker to convert Convert 17 to a percent than the previous problems? 20 17 to a percent. Show work. 20 Obj. 2 Convert percent to fraction notation Find fraction notation for 62.5% Write fraction notation for 16. 6 % Module 4E – 6.4 and 16.3 6.4 - Solving percent problems using percent equations Objective 1. Translate percent problems to percent equations Key words in percent translations: “Of” translates to _____________________________ “is” translates to _____________________________ “What” translates to _____________________________ “%” translates to _____________________________ Examples: Translate this problem to equation: 1) What is 32% of 78? 2) 13 is 25% of what? STOP THE VIDEO AND ANSWER THE FOLLOWING QUESTIONS. CONTINUE WITH THE VIDEO AFTER THE QUESTIONS ARE ANSWERED: When translating to a percent equation, you must write the percent in decimal notation using the "X 0.01" rule. So, in the above example, 32% should be written as 32 X 0.01 or .32. How should 25% be written? Write each of the equations above using decimal notation in place of percent notation: 1) 2) Objective 2. Solve basic percent problems Types of percent problems: 1. Finding the _____________________________________ (result of taking percent) Solve: What is 6% of $300? 2. Finding the ______________________________________ (number you are taking percent of) Solve: 56.32 is 64% of what? 3. Finding the ______________________________________ (the percent itself) Solve: What percent of $50 is $16? 16.3 Simplify Square Roots of Perfect Squares of Decimals List the steps for simplifying square roots of decimals and work the examples with the video. Example 1: .0016 (This first example will be worked out as the steps are explained.) 1. 2. 3. 4. Example 2: .000064