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Scientific notation usage in chemistry contexts - Health Education Systems Admission Assessment HESI

  1. A calculation involving molecular concentration yields the result 453.7×10−9453.7 \times 10^{-9} M. How should this result be expressed in proper scientific notation?
    Answer: 4.537×10−74.537 \times 10^{-7} M When you encounter scientific notation problems on the HESI, you're being tested on your ability to express very large or very small numbers in standard form, which is crucial for medical calculations involving drug concentrations, lab values, and dosages. To convert 453.7×10−9453.7 \times 10^{-9} M to proper scientific notation, you need to adjust the coefficient to fall between 1 and 10. Currently, your coefficient is 453.7, which is too large. To fix this, move the decimal point two places to the left: 453.7 becomes 4.537. When you move the decimal point left by two places, you must add 2 to the exponent to maintain the number's value. So −9+2=−7-9 + 2 = -7, giving you 4.537×10−74.537 \times 10^{-7} M. Answer B (4.537×10−74.537 \times 10^{-7} M) is correct because it properly expresses the number with a coefficient between 1 and 10. Answer A (4.537×10−114.537 \times 10^{-11} M) represents a common error where students subtract 2 from the exponent instead of adding it when moving the decimal left. Answer C (45.37×10−845.37 \times 10^{-8} M) shows partial conversion—the decimal was moved only one place, leaving the coefficient still outside the proper range. Answer D (4.537×10−64.537 \times 10^{-6} M) results from incorrectly adding 3 to the exponent instead of 2. Remember this rule: when converting to scientific notation, moving the decimal point left means adding to the exponent, while moving it right means subtracting from the exponent. Always ensure your final coefficient falls between 1 and 10.
  2. The wavelength of a particular ultraviolet (UV) light used for sterilization is 254 nm. What is this wavelength expressed in kilometers (km)? (1 m = 1×1091 \times 10^9 nm; 1 km = 1×1031 \times 10^3 m).
    Answer: 2.54×10−102.54 \times 10^{-10} km Unit conversion problems test your ability to systematically work through multiple conversion factors while maintaining proper scientific notation. When converting between units that differ by many orders of magnitude, like nanometers to kilometers, you need to carefully track each step and watch your exponents. To convert 254 nm to kilometers, you'll use the given conversion factors sequentially. First, convert nanometers to meters: 254 nm×1 m1×109 nm=2541×109 m=2.54×10−7 m254 \text{ nm} \times \frac{1 \text{ m}}{1 \times 10^9 \text{ nm}} = \frac{254}{1 \times 10^9} \text{ m} = 2.54 \times 10^{-7} \text{ m} Next, convert meters to kilometers: 2.54×10−7 m×1 km1×103 m=2.54×10−71×103 km=2.54×10−10 km2.54 \times 10^{-7} \text{ m} \times \frac{1 \text{ km}}{1 \times 10^3 \text{ m}} = \frac{2.54 \times 10^{-7}}{1 \times 10^3} \text{ km} = 2.54 \times 10^{-10} \text{ km} This confirms answer A is correct. Answer B (2.54×10−92.54 \times 10^{-9} km) results from only converting nm to m but forgetting the second step to kilometers. Answer C (2.54×10−42.54 \times 10^{-4} km) likely comes from incorrectly manipulating the exponents during conversion, perhaps adding instead of subtracting. Answer D (2.54×1042.54 \times 10^{4} km) represents a fundamental error in conversion direction—this would make the UV wavelength enormous, about 25,000 kilometers! For HESI unit conversion problems, always write out each conversion step separately and double-check that your final answer makes physical sense. A UV wavelength should be extremely small when expressed in kilometers.
  3. A student records four measurements in a lab notebook. Which of the following measurements represents the smallest mass?
    Answer: 0.025 g When comparing masses across different units, you need to convert everything to the same unit to make accurate comparisons. This question tests your ability to work with scientific notation and unit conversions simultaneously. Let's convert all measurements to grams for easier comparison: For choice A: 2.5×10−42.5 \times 10^{-4} kg = 2.5×10−4×10002.5 \times 10^{-4} \times 1000 g = 2.5×10−12.5 \times 10^{-1} g = 0.25 g For choice B: 2.5×1022.5 \times 10^{2} mg = 2.5×102×0.0012.5 \times 10^{2} \times 0.001 g = 2.5×10−12.5 \times 10^{-1} g = 0.25 g For choice C: 2.5×1052.5 \times 10^{5} μg = 2.5×105×10−62.5 \times 10^{5} \times 10^{-6} g = 2.5×10−12.5 \times 10^{-1} g = 0.25 g Choice D is already in grams: 0.025 g Comparing the results: 0.025 g < 0.25 g, so choice D represents the smallest mass. Choice A appears smaller due to the negative exponent, but when you account for kilograms being 1000 times larger than grams, it equals 0.25 g. Choice B might seem large because of the positive exponent, but milligrams are much smaller units than grams. Choice C has the largest-looking number due to scientific notation, but micrograms are tiny units, so this also equals 0.25 g. Remember this strategy: when comparing measurements in different units, always convert to a common unit first. Pay attention to both the numerical value and the unit size—a smaller number with a larger unit can represent more than a larger number with a smaller unit.
  4. The radius of a sodium atom (Na) is 1.86×10−101.86 \times 10^{-10} meters, while the radius of a sodium ion (Na⁺) is 1.02×10−101.02 \times 10^{-10} meters. What is the difference in their radii, expressed in proper scientific notation?
    Answer: 8.4×10−118.4 \times 10^{-11} m When you encounter scientific notation problems involving subtraction, you need to perform the arithmetic operation first, then express the result in proper scientific notation format. To find the difference in radii, subtract the sodium ion radius from the sodium atom radius: 1.86×10−10−1.02×10−10=0.84×10−101.86 \times 10^{-10} - 1.02 \times 10^{-10} = 0.84 \times 10^{-10} meters. Since both numbers have the same power of 10, you can directly subtract the coefficients. However, 0.84×10−100.84 \times 10^{-10} is not in proper scientific notation because the coefficient must be between 1 and 10. To convert this, move the decimal point one place to the right and decrease the exponent by 1: 0.84×10−10=8.4×10−110.84 \times 10^{-10} = 8.4 \times 10^{-11} meters, which is answer choice B. Looking at the wrong answers: Choice A (0.84×10−100.84 \times 10^{-10}) shows the correct arithmetic but fails to convert to proper scientific notation. Choice C (8.4×10−108.4 \times 10^{-10}) represents a common error where students correctly adjust the coefficient to 8.4 but mistakenly keep the original exponent instead of reducing it by 1. Choice D (8.4×10−98.4 \times 10^{-9}) shows confusion about exponent direction—increasing rather than decreasing the power of 10. Remember: proper scientific notation requires a coefficient between 1 and 10. When you move the decimal point right to increase the coefficient, you must decrease the exponent by the same number of places moved. Always double-check that your final answer follows this format.

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