Problem 35
Round off each of the following numbers to the indicated number of significant digits, and write the answer in standard scientific notation. a. 0.00034159 to three digits b. \(103.351 \times 10^{2}\) to four digits c. 17.9915 to five digits d. \(3.365 \times 10^{5}\) to three digits
Problem 36
Use exponential notation to express the number 385,500 to a. one significant figure. b. two significant figures. c. three significant figures. d. five significant figures.
Problem 39
Evaluate each of the following, and write the answer to the appropriate number of significant figures. a. \(212.2+26.7+402.09\) b. \(1.0028+0.221+0.10337\) c. \(52.331+26.01-0.9981\) d. \(2.01 \times 10^{2}+3.014 \times 10^{3}\) e. \(7.255-6.8350\)
Problem 40
Perform the following mathematical operations, and express each result to the correct number of significant figures. a. \(\frac{0.102 \times 0.0821 \times 273}{1.01}\) b. \(0.14 \times 6.022 \times 10^{23}\) c. \(4.0 \times 10^{4} \times 5.021 \times 10^{-3} \times 7.34993 \times 10^{2}\) d. \(\frac{2.00 \times 10^{6}}{3.00 \times 10^{-7}}\)
Problem 41
Perform the following mathematical operations, and express the result to the correct number of significant figures. a. \(\frac{2.526}{3.1}+\frac{0.470}{0.623}+\frac{80.705}{0.4326}\) b. \((6.404 \times 2.91) /(18.7-17.1)\) c. \(6.071 \times 10^{-5}-8.2 \times 10^{-6}-0.521 \times 10^{-4}\) d. \(\left(3.8 \times 10^{-12}+4.0 \times 10^{-13}\right) /\left(4 \times 10^{12}+6.3 \times 10^{13}\right)\) e. \(\frac{9.5+4.1+2.8+3.175}{4}\) (Assume that this operation is taking the average of four numbers. Thus 4 in the denominator is exact.) f. \(\frac{8.925-8.905}{8.925} \times 100\) (This type of calculation is done many times in calculating a percentage error. Assume that this example is such a calculation; thus 100 can be considered to be an exact number.)
Problem 42
Perform the following mathematical operations, and express the result to the correct number of significant figures. a. \(6.022 \times 10^{23} \times 1.05 \times 10^{2}\) b. \(\frac{6.6262 \times 10^{-34} \times 2.998 \times 10^{8}}{2.54 \times 10^{-9}}\) c. \(1.285 \times 10^{-2}+1.24 \times 10^{-3}+1.879 \times 10^{-1}\) d. \(\frac{(1.00866-1.00728)}{6.02205 \times 10^{23}}\) e. \(\frac{9.875 \times 10^{2}-9.795 \times 10^{2}}{9.875 \times 10^{2}} \times 100(100 \text { is exact) }\) f. \(\frac{9.42 \times 10^{2}+8.234 \times 10^{2}+1.625 \times 10^{3}}{3}(3 \text { is exact) }\)
Problem 43
Perform each of the following conversions. a. 8.43 \(\mathrm{cm}\) to millimeters b. \(2.41 \times 10^{2} \mathrm{cm}\) to meters c. 294.5 \(\mathrm{nm}\) to centimeters d. \(1.445 \times 10^{4} \mathrm{m}\) to kilometers e. 235.3 \(\mathrm{m}\) to millimeters f. 903.3 \(\mathrm{nm}\) to micrometers
Problem 44
a. How many kilograms are in 1 teragram? b. How many nanometers are in \(6.50 \times 10^{2}\) terameters? c. How many kilograms are in 25 femtograms? d. How many liters are in 8.0 cubic decimeters? e. How many microliters are in 1 milliliter? f. How many picograms are in 1 microgram?
Problem 45
Perform the following unit conversions. a. Congratulations! You and your spouse are the proud parents of a new baby, born while you are studying in a country that uses the metric system. The nurse has informed you that the baby weighs 3.91 kg and measures 51.4 cm. Convert your baby’s weight to pounds and ounces and her length to inches (rounded to the nearest quarter inch). b. The circumference of the earth is 25,000 mi at the equator. What is the circumference in kilometers? in meters? c. A rectangular solid measures 1.0 m by 5.6 cm by 2.1 dm. Express its volume in cubic meters, liters, cubic inches, and cubic feet.
Problem 46
Perform the following unit conversions. a. \(908 \mathrm{oz}\) to kilograms b. \(12.8 \mathrm{~L}\) to gallons c. \(125 \mathrm{~mL}\) to quarts d. 2.89 gal to milliliters e. 4.48 lb to grams f. \(550 \mathrm{~mL}\) to quarts
