TOPICS COVERED ON “NUMBER SENSE” TEST: Name: Date: Math-7 Study Guide “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 COVERED ON “NUMBER SENSE” TEST: Converting among Fractions, Decimals, and Percents Scientific Notation (both large AND small #’s– positive exponent and negative exponent) Comparing Rational #’s (“greater than” or “less than”) Ordering Rational #’s (mixture of fractions, decimals, %’s, scientific notation) General Fraction, Decimal, % Word Problems Exponents Perfect Square #’s and Square Roots NOTES SPACE/HELPFUL TIPS (to be filled out in class):
“Take the top #, Divide by the bottom #!” Converting fractions, decimals, and percents 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 right, to the right!” “To the left, to the left!” Converting between Percents and Decimals: Converting a Fraction to a Decimal: “Take the top #, Divide by the bottom #!” Converting a Decimal to a Fraction: READ IT, ______________ IT, REDUCE IT!!! Fraction Decimal Percent 1. 7/8 2. 0.05 45% 4. 1/3 5. 0.4 6. 25 % 7. 3/5 8. 6.2 9. 9.5% 10. 5/11
Scientific notation Standard Form Scientific Notation 1. 6,230,000 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. .00015 1.5 x 10-4 4. .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. .000025 11. 1.2 x 10 4 12. 2.789 x 10 3 13. 93,000 14. .017 15. 8.3 x 10 0 16. 7.7 x 10 -4 17. 9,240,000,000 18. .00019 19. 3.6 x 10 1 20. 8.4 x 10 -4
COMPARING DECIMAL NUMBERS Directions: Look at the below examples. Then, complete #’s 1 – 10: Arrange the following decimals in order of size, from smallest to largest. You may wish to attach zeros at the end in order to compare.
(List in Original Form): Ordering rational NUMBERS Order the following #’s in the order indicated: # Fraction Decimal % Scientific Notation Answer (List in Original Form): 1. 2/3 0.6 59% 6.6 x 10-2 Least to Great: 2. 11/8 1.2 1.12% 1.125 x 103 Greatest to Least: Multiple Choice: 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 6. 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 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. 73 8. 34 9. 182 10. 60 11. 26 12. 83 Evaluate the following powers with negative exponents: 13. 7-2 14. 3-3 15. 15-2 16. 4-3 17. 2-4
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 9 400 225 361 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? __________
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 1