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Difficulty: EasyScientific Notation and Unit Conversions

In an environmental science study, a student collects a sample of airborne particulate matter and determines its mass to be 8.5×10−6 grams8.5 \times 10^{-6}\text{ grams}. Which of the following is equivalent to this mass expressed in milligrams (mg\text{mg})?

  1. A
    8.5×10−9 mg8.5 \times 10^{-9}\text{ mg}
  2. 8.5×10−3 mg8.5 \times 10^{-3}\text{ mg}Answer
  3. C
    8.5×10−5 mg8.5 \times 10^{-5}\text{ mg}
  4. D
    8.5×103 mg8.5 \times 10^{3}\text{ mg}

Answer

8.5×10−3 mg8.5 \times 10^{-3}\text{ mg}
To convert from grams to milligrams, the given mass in grams must be multiplied by 10310^3 (since 1 gram=1,000 milligrams1\text{ gram} = 1,000\text{ milligrams}). Carrying out this operation: (8.5×10−6)×103=8.5×10−6+3=8.5×10−3 mg(8.5 \times 10^{-6}) \times 10^3 = 8.5 \times 10^{-6 + 3} = 8.5 \times 10^{-3}\text{ mg}. This value is the correct equivalent mass.

Step-by-Step Solution

1
Identify the conversion factor between grams and milligrams.
Since 1 gram=103 milligrams1\text{ gram} = 10^3\text{ milligrams}, the conversion factor is 103 mg/g10^3\text{ mg/g}.
Establishing the relationship between the units is necessary to perform the conversion.
2
Multiply the given mass by the conversion factor.
(8.5×10−6 g)×(103 mg/g)(8.5 \times 10^{-6}\text{ g}) \times (10^3\text{ mg/g})
Multiplying the value in grams by the number of milligrams per gram converts the unit to milligrams.
3
Simplify the expression by adding the exponents of the base 10 terms.
8.5×10−6+3=8.5×10−3 mg8.5 \times 10^{-6 + 3} = 8.5 \times 10^{-3}\text{ mg}
Applying the laws of exponents (adding exponents when multiplying powers of the same base) yields the final answer in scientific notation.

Key Concept

Scientific Notation and Unit Conversions
Estimated Time:45s
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Topics

Scientific Notation and Unit Conversions

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