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Massaging Scientific Notation Name_____ANSWERS_________________ Directions: Perform the following operations and cross out your answers in the table at the end. Be sure to finish the last question at the end. 1. Which is the larger value: 3 10 or 9 10 ? 8 7 2. How much times larger is 8 10 compared to 4 10 ? 200 times (8 is two times larger than 4 and 106 is 100 times larger than 104) 6 4 3. The planet Venus is 26 million miles away from Earth at its closest point and 160 million miles away at this most distant point. What is the difference between these distances, expressed in 8 scientific notation? 160,000,000 – 26,000,000 = 134,000,000 miles = 1.34 10 4. Multiply: 7.25 10 4.12 10 29.87 10 9 14 5 2.987 1015 4.5 109 5. Divide: 3 104 5 1.5 10 6. Multiply: 0.0035 4.2 10 3.5 10 4.2 10 14.7 10 3 2 8.2 10 5.0 10 20.5 10 Simplify: 2.0 10 5 1.47 10 6 2 6 7. 2 2.05 103 2 2 8. The Earth is 93 million miles from the sun. How long, in seconds, does it take light from the sun to 5 reach Earth? Use the speed of light to be 1.86 10 miles per second. 9.3 107 5.0 102 500 seconds 5 1.86 10 9. Which of the following expressions is equivalent to: 1) 14.2 100 2) 14.2 3) 1.42 10 1 0.5 10 28.4 10 45 45 4) All of these are equivalent. 5 10. Which of the following expression is 145.87 10 in scientific notation? 3 4 6 7 1) 1.4587 10 2) 1.4587 10 3) 1.4587 10 4) 1.4587 10 All Rights Reserved © MathBits.com 11. The expression 0.00222 10 is greater than 2 (and n is an integer). What is the smallest possible value for n? 3 n 12. A rectangle has a length of 12.2 10 mm and a width of 6.5 10 mm. Expressed in scientific notation, how many square mm are in the area of the rectangle? 3 12.2 10 6.5 10 79.3 10 3 2 2 7.93 106 5 13. If a CD can store 700,000,000 bytes of data, express, in scientific notation, the number of bytes of 9 data which can be stored on 2 such CDs. 1.4 10 6.8 105 8 14. Divide: 2.0 10 3 3.4 10 15. Multiply: 4.3 10 3.1 10 13.33 10 4 7 11 1.333 1010 Numbers in scientific notation can be added if the ten’s exponents are the same in each number. Simply add the decimal numbers and keep the power of 10. If necessary, adjust the numbers such that 4 4 4 these exponents are the same. Example: 3.1 10 6.5 10 9.6 10 16. Add: 8.2 10 4.7 10 12.9 10 6 6 6 17. Add: 9.1 10 1.8 10 91.0 10 1.8 10 92.8 10 9.28 10 8 7 7 7 7 8 Cross OUT your answers. 200 400 500 2.0 102 2.0 108 3 104 3 108 1.34 108 1.333 1010 12.9 1012 12.9 106 1 2 3 4 2.987 1015 2.987 1014 10.9 1015 2.05 103 9.28 108 14 108 1.4 109 79.3 105 7.93 106 1.47 106 Multiply the remaining answers. Express the result in scientific notation: ____________ 7.46058077 10 ______________ 60 All Rights Reserved © MathBits.com