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Scientific notation Transitional Reasoning Practice

Math · Number Sense & Operations · Math · Exponents & Scientific Notation

4 Math practice questions on Scientific notation. Questions that build towards applied reasoning.

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Questions

  1. 1.

    A planetary rover collects a core sample of subsurface rock with a mass of 4.5×10−14.5 \times 10^{-1} kilograms and a volume of 1.8×10−41.8 \times 10^{-4} cubic meters. Orbital radar scans indicate that the continuous geological formation from which the sample was extracted has a uniform composition and a total estimated volume of 3.2×1053.2 \times 10^5 cubic meters. Based on this data, what is the estimated total mass of the geological formation in kilograms, expressed in scientific notation?

    • A) 7.2×108 kg7.2 \times 10^8\text{ kg}
    • B) 8.0×107 kg8.0 \times 10^7\text{ kg}
    • C) 8.0×108 kg8.0 \times 10^8\text{ kg}
    • D) 8.0×109 kg8.0 \times 10^9\text{ kg}
  2. 2.

    An environmental monitoring facility tests a reservoir containing 1.25×1081.25 \times 10^8 liters of water, where sensors detect an average of 4.8×1034.8 \times 10^3 microplastic particles per liter. A newly installed ultra-fine filtration system is designed to capture 95%95\% of these microplastic particles during the purification cycle. How many microplastic particles will remain in the reservoir water after this filtration process is completed, expressed in scientific notation?

    • A) 3.0×1093.0 \times 10^9
    • B) 5.7×10115.7 \times 10^{11}
    • C) 3.0×10103.0 \times 10^{10}
    • D) 6.0×10106.0 \times 10^{10}
  3. 3.

    A satellite communications center records that ground station Alpha received 8.4×10118.4 \times 10^{11} bytes of telemetry data during a mission, whereas ground station Beta received 9.6×10109.6 \times 10^{10} bytes. To balance network traffic, engineers calculate the positive difference between these two data volumes and distribute it equally among 1.5×1041.5 \times 10^4 storage nodes. How many bytes of data are allocated to each storage node, expressed in scientific notation?

    • A) 5.536×1075.536 \times 10^7
    • B) 6.24×1076.24 \times 10^7
    • C) 4.96×1084.96 \times 10^8
    • D) 4.96×1074.96 \times 10^7
  4. 4.

    A specialized micro-fabrication system deposits 2.5×1062.5 \times 10^6 filament clusters per hour, where each cluster has an average mass of 3.6×10−83.6 \times 10^{-8} grams. If the system operates continuously for a total lifespan of 4.8×1044.8 \times 10^4 hours, what is the total mass of the deposited clusters in grams, expressed in scientific notation?

    • A) 4.32×1014.32 \times 10^1 grams
    • B) 4.32×1034.32 \times 10^3 grams
    • C) 4.32×1024.32 \times 10^2 grams
    • D) 4.32×1044.32 \times 10^4 grams

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