Unit 1 Test, “Number Sense” Name:____________________________________________________________________________________Date:_____/_____/__________ Study Guide/ Practice Unit 1 Test, “Number Sense” Note: Many problems in this packet will be completed together in class during review time. Students are not expected to complete every single problem in the packet. They should complete several problems from each page-- in addition to studying the notes and past quizzes– in order to be fully prepared for test. Topics: Converting among Fractions, Decimals, and Percentages Comparing Rational #’s (“greater than” or “less than”) Ordering Rational #’s (mixture of fractions, decimals, %’s, scientific notation) Exponents Perfect Square #’s and Square Roots Scientific Notation (positive exponents and negative exponents) On the back of this cover page is the Unit 1 “Quick Guide” – for your reference.

Unit 1, “Number Sense,” Quick Guide Fraction  Decimal “Take the top #, divide by the bottom #!” 1 = 8 I 1 8 (turn the fraction clockwise) Negative exponents do NOT make the answer negative!! Exponents: 10 3 = 10 x 10 x 10 = 1,000 10 -3 = 1 10 x 1 10 x 1 10 = 1 1000 = 0.001 Square Root Examples: 𝟐𝟓 = 5 x 5 = 5 𝟑𝟔 = 6 x 6 = 6 𝟒𝟗 = 7 x 7 = 7

Divide by the __________ #!” Converting fractions, decimals, and percentages A B C D E F G H I J K L M N O P Q R S T U V W X Y Z “To the ________, to the right!” “To the _______, to the left!” Converting between Percents and Decimals: Converting a Fraction to a Decimal: “Take the ______ #, Divide by the __________ #!” Converting a Decimal to a Fraction: READ IT, ______________ IT, REDUCE IT!!! SHOW YOUR WORK! Fraction Decimal Percent 1. 7/8 2. 0.05 45% 4. 1/3 5. 6.2 6. 9.5% 7. 3/5 8. 75% = 3 4 75 100 75 1000 0.75 7.5 7,500 9. 0.6 = 60% 6% 3 5 6 100 60 100 6 10

(List in Original Form): COMPARING & Ordering rational NUMBERS Order the following #’s in the order indicated: # Fraction Decimal % Answer (List in Original Form): 1) 2/3 0.6 59% ASCENDING (Least to Greatest): 2. 11/8 1.2 1.12% DESCENDING (Greatest to Least): Place a > sign, a < sign, or an = sign in the following blanks: 3) 0.8 ________ 55% 5) 40% ________ 0.04 4) 3/4 ________ 0.7 6) 20% ________ 1/5 Circle the answer that makes the following true: 7) 25% < ________ < 0.7 A. 70% B. 0.035 C. 0.3 8) 0.05 < ________ < 1/2 A. 0.5 B. 0.25 C. 0.025 Multiple Choice. Circle the correct answer. SHOW YOUR WORK! Which of the following is equivalent to 5/8 ? A. 62.5 B. 62.5% C. 6.25 x 10-3 D. 5.8 Four students recorded their scores on a quiz in different ways. Which score is the highest? A. 80% B. 0.09 C. 9/100 D. 9/10 Which of the following is equivalent to 0.75? A. 75% B. 75/10 C. 7.5 x 10-2 D. 75 Jerry got a 41/50 on his math test. What is his grade as a percentage? A. 41% B. 78% C. 82% D. 80%

Exponents & Powers of 10 Fill in the following powers of 10 chart : 1010= 10,000,000,000 105= __________________ 100= __________________ 109= _________________ 104= __________________ 10-1= __________________ 108= _________________ 103= __________________ 10-2= __________________ 107= __________________ 102= __________________ 10-3= __________________ 106= __________________ 101= __________________ 10-4= _________________ Evaluate the following powers of 10 (use the pattern . . .): 1. 1014 2. 1012 3. 100 Evaluate the following powers of 10 with negative exponents. You must give both the fraction and decimal form: 4. 10-2 5. 10-4 6. 10-5 Evaluate the following powers with positive exponents: 7. 53 8. 34 9. 150 10. 60 11. 26 12. 43 Evaluate the following powers with negative exponents: 13. 7-2 14. 3-3 15. 4-3 16. 10-5 = 1 10 x 1 10 x 1 10 x 1 10 x 1 10 1 10,000 0.000001 0.00001 10 x 10 x 10 x 10 x 10 -10,000 17. 102 = 1 10 x 1 10 20 10 x 10 100 -100 0.01

Perfect square #’s and square roots Fill in the missing information in the below “perfect square” table: 12 = _____ 62 = _____ 112 = _____ 162 = _____ 22 = _____ 72 = _____ 122 = _____ 172 = _____ 32 = _____ 82 = _____ 132 = 169 182 = 324 42 = 16 92 = 81 142 = _____ 192 = _____ 52 = _____ 102 = _____ 152 = _____ 202 = _____ Find the square root of the following numbers : 1. = __________ 2. = __________ 3. = __________ 4 . = __________ 5. = __________ 6. = __________ 7 . = __________ 8. = __________ 9. = __________ 10 . = __________ 11. = __________ 12. = __________ 169 100 121 36 400 225 361 c Between which two consecutive WHOLE numbers do the following #’s fall between?: 13. lies between __________ and __________. 14. lies between __________ and __________. 15. lies between __________ and __________. 16. lies between __________ and __________. 10 215 40 95 17. Bob wants to plant a square garden. The area of the garden will be 86 sq. ft. About how long will each side be? __________ 18. What perfect square # does the square to the right represent? __________ What is its square root? __________

Scientific notation Standard Form Scientific Notation Convert between scientific notation and standard form. A few examples are done for you. Standard Form Scientific Notation 1. 6,230,000 6.23 x 106 2. 8,200 3. 0.00015 1.5 x 10-4 4. 0.000027 5. 61,000 6.1 x 10 4 6. 7.02 x 10 3 7. 0.0092 9.2 x 10 -3 8. 5.26 x 10 -5 9. 2,680,000 10. 0.000025 11. 1.2 x 10 4 12. 2.789 x 10 3 13. 93,000 14. 0.017 15. 8.3 x 10 0 16. 7.7 x 10 -4 17. 9,240,000,000 18. 0.00019 19. 3.6 x 10 1 20. 8.4 x 10 -4 Order the following from least to greatest: 21) 3.05 x 105 9.845 x 102 6.1 x 109 5.7 x 105 Answer: 22) 8.3 x 10-5 1.68 x 107 2.25 x 104 4 x 104 Answer:

Miscellaneous Multiple Choice:

Place the following numbers in the correct spot on the below number line: 0.75 40% 0.01 1/10 80% 1/4