Writing Numbers in Scientific Notation, Exams of Science education

Download Writing Numbers in Scientific Notation and more Exams Science education in PDF only on Docsity! Writing Numbers in Scientific Notation To write a number in scientific notation 1. Move the decimal point right or left to obtain a number n such that 1 < n < 10. 2. Count the number of places p that the decimal point has been moved. 3. Multiply n by 10p if the decimal point was moved to the left. Multiply n by 10-p if the decimal point was moved to the right. Be sure to eliminate any meaningless zeros. Example 1 Write in scientific notation: a. 10,300,000 b. 0.00089 Solution a. We need to move the decimal point to the left 7 places to get a number n such that 1 < n < 10. 10300000 = 1.0300000 So we multiply n by 107. The zeros to the right of the 3 are meaningless, so we eliminate them, getting 1.03 x 107 b. We need to move the decimal point to the right 4 places to obtain a number n such that 1 < n < 10. Then we multiply the result by 10-4 and eliminate the meaningless zeros on the left. 0.00089 = 00008.9 x 10-4 = 8.9 x 10-4 To write a number in standard notation 1. Move the decimal point the number of places, p, in 10p. Move it to the right if the exponent is positive; move it to the left if the exponent is negative. (Add zeros as necessary.) 2. Eliminate the multiplication sign and power of 10. Example 2 Write in standard notation: a. 1.206 x 109 b. 3.05 x 10-7 Solution a. Because the exponent is 9, we move the decimal point 9 places to the right. 1.206 x 109 = 1.206000000 = 1,206,000,000 b. Because the exponent is -7, we must move the decimal point 7 places to the left. 3.05 x 10-7 = .000000305 = 0.000000305 Example 3 a. (4.8 x 1015) x (6.4 x 1012) b. Divide the first of these numbers by the second. Solution a. To multiply two numbers in scientific notation, multiply the coefficients and then the powers of 10. (4.8 x 1015)(6.4 x 1012) = (4.8)(6.4) x 10(15+12) = 30.72 x 1027 This number is not in scientific notation because 30 > 10. To write it correctly, we put the decimal part in the proper scientific notation and then simplify. 30.72 x 1027 = (3.072 x 101) x 1027 = 3.072 x 1028 b. To divide in scientific notation, we divide the coefficients and then subtract the powers of 10. 4.8 x 1015 4.8 = x 10(15-12) 6.4 x 1012 6.4 = 0.75 x 103 = (07.5 x 10-1) x 102 Practice: Rewrite each number in scientific notation: 1. Number of pounds of advertising mail received by Americans in one year: 3,650,000,000 pounds 2. A red blood cell count is typically about 5,000,000/mm3 blood. Express this count in scientific notation. 3. The average human brain is believed to have about 100 billion nerve cells. Express this in scientific notation. 4. 0.000072 0.008 5. Time needed to compress a deuterium pellet by laser light: 0.000000001 second 6. Size of a DNA molecule: 0.00000217 millimeter Rewrite each number in standard notation: 7. Energy given off by a hurricane: 5.0 x 1022 ergs 8. Number of gallons of water used by Americans daily: 4.5 x 1011 gallons 9. The pH value of a certain chemical is 1.0 x 10-2. 10. Number of seconds in the month of January: 2.6784 x 106 seconds 11. An x-ray has a wavelength of 1 x 10-10