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MATH 0925 MODULE 6 EXAM STUDY PACK TOPICS COVERED: * Decimals * Place Value * Expanded Form * Word Form * Standard Form * Rounding * Decimals to Fractions * Fractions to Decimals * Comparing and Ordering Decimals * Perfect Squares * Square Roots * Rational and Irrational Numbers * Adding Decimals * Subtracting Decimals * Multiplying Decimals * Dividing Decimals * Mean * Median * Mode * Range FLASHCARDS Q: What is the tenths place? A: The first digit to the right of the decimal. Q: What is the hundredths place? A: The second digit to the right of the decimal. Q: What is the thousandths place? A: The third digit to the right of the decimal. Q: Write 0.352 in expanded form. A: 3(0.1) + 5(0.01) + 2(0.001) Q: Write 4.2706 in expanded form. A: 4 + 2(0.1) + 7(0.01) + 6(0.0001) Q: How do you write a decimal in word form? A: Read the whole number, say “and,” then read the decimal part and its place value. Q: Write 24.9 in word form. A: Twenty-four and nine tenths. Q: How do you round decimals? A: Look at the digit to the right of the rounding place. Q: What happens when the next digit is 5 or more? A: Round up. Q: What happens when the next digit is less than 5? A: Keep the digit the same. Q: Convert 0.46 to a fraction. A: 46/100 = 23/50. Q: Convert 0.12 to a fraction. A: 12/100 = 3/25. Q: Convert 0.105 to a fraction. A: 105/1000 = 21/200. Q: How do you convert a fraction to a decimal? A: Divide numerator by denominator. Q: How do you compare decimals? A: Compare digits from left to right. Q: Which is greater, 0.20 or 0.12? A: 0.20. Q: Which is greater, -8 or -9? A: -8. Q: What is 1²? A: 1. Q: What is 2²? A: 4. Q: What is 3²? A: 9. Q: What is 4²? A: 16. Q: What is 5²? A: 25. Q: What is 6²? A: 36. Q: What is 7²? A: 49. Q: What is 8²? A: 64. Q: What is 9²? A: 81. Q: What is 10²? A: 100. Q: What is 11²? A: 121. Q: What is 12²? A: 144. Q: What is √36? A: 6. Q: What is √49? A: 7. Q: What is √81? A: 9. Q: What is √121? A: 11. Q: What is √(16/49)? A: 4/7. Q: Is √(-100) a real number? A: No. It is not a real number. Q: What is a rational number? A: A decimal that stops or repeats. Q: What is an irrational number? A: A decimal that never stops and never repeats. Q: Is π rational or irrational? A: Irrational. Q: Is √2 rational or irrational? A: Irrational. Q: What is the rule for adding decimals? A: Line up decimal points. Q: What is the rule for subtracting decimals? A: Line up decimal points. Q: What is the rule for multiplying decimals? A: Multiply normally and count decimal places. Q: What is the rule for dividing decimals? A: Make the divisor a whole number. Q: What is the mean? A: Average. Q: How do you find the mean? A: Add all values and divide by the number of values. Q: What is the median? A: The middle value after ordering the data. Q: What is the mode? A: The value that appears most often. Q: What is the range? A: Largest value minus smallest value. IMPORTANT EXAM RULES 1. Line up decimals when adding and subtracting. 2. Count decimal places when multiplying. 3. Make the divisor a whole number before dividing. 4. Memorize perfect squares from 1² through 12². 5. Rational numbers stop or repeat. 6. Irrational numbers never stop and never repeat. 7. Mean = Average. 8. Median = Middle. 9. Mode = Most Common. 10. Range = Largest − Smallest. COMMON MISTAKES * Forgetting to line up decimals. * Forgetting to simplify fractions. * Mixing up mean and median. * Forgetting to count decimal places in multiplication. * Forgetting to move BOTH decimals in division. * Thinking all square roots are rational. * Forgetting that negative numbers closer to zero are larger. PRACTICE QUESTIONS 1. Round 45.0193 to the nearest hundredth. Answer: 45.02 2. Convert 0.36 to a fraction. Answer: 9/25 3. Convert 3/8 to a decimal. Answer: 0.375 4. Which is larger: 0.205 or 0.25? Answer: 0.25 5. Find √64. Answer: 8 6. Is √5 rational or irrational? Answer: Irrational 7. Add: 14.563 + 6.29 Answer: 20.853 8. Subtract: 24 − 8.0731 Answer: 15.9269 9. Multiply: 4.8 × 0.13 Answer: 0.624 10. Find the mean of 10, 20, 30. Answer: 20

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