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Difficulty: MediumDecimals and Scientific Notation

A laboratory mixture is created by combining two solutions containing a specific tracer compound. Solution X has a volume of 2.5×1032.5 \times 10^3 milliliters and a tracer concentration of 4.8×10−74.8 \times 10^{-7} grams per milliliter. Solution Y has a volume of 7.5×1037.5 \times 10^3 milliliters and a tracer concentration of 1.6×10−61.6 \times 10^{-6} grams per milliliter. What is the total mass, in grams, of the tracer compound present in the combined mixture?

  1. 1.32×10−21.32 \times 10^{-2}Answer
  2. B
    2.4×10−32.4 \times 10^{-3}
  3. C
    1.32×10−51.32 \times 10^{-5}
  4. D
    2.4×10−22.4 \times 10^{-2}
  5. E
    1.32×10−11.32 \times 10^{-1}

Answer

1.32×10−21.32 \times 10^{-2} grams
The mass in Solution X is (2.5×103)×(4.8×10−7)=1.2×10−3(2.5 \times 10^3) \times (4.8 \times 10^{-7}) = 1.2 \times 10^{-3} grams, and the mass in Solution Y is (7.5×103)×(1.6×10−6)=1.2×10−2(7.5 \times 10^3) \times (1.6 \times 10^{-6}) = 1.2 \times 10^{-2} grams. Rewriting 1.2×10−31.2 \times 10^{-3} as 0.12×10−20.12 \times 10^{-2} allows direct addition: (0.12+1.2)×10−2=1.32×10−2(0.12 + 1.2) \times 10^{-2} = 1.32 \times 10^{-2} grams.

Step-by-Step Solution

1
Calculate the mass of the tracer in Solution X
MX=(2.5×103)×(4.8×10−7)=12.0×10−4=1.2×10−3M_X = (2.5 \times 10^3) \times (4.8 \times 10^{-7}) = 12.0 \times 10^{-4} = 1.2 \times 10^{-3} grams
Mass equals volume multiplied by concentration.
2
Calculate the mass of the tracer in Solution Y
MY=(7.5×103)×(1.6×10−6)=12.0×10−3=1.2×10−2M_Y = (7.5 \times 10^3) \times (1.6 \times 10^{-6}) = 12.0 \times 10^{-3} = 1.2 \times 10^{-2} grams
Mass equals volume multiplied by concentration.
3
Sum the tracer masses and adjust to scientific notation
Mtotal=1.2×10−3+1.2×10−2=0.12×10−2+1.2×10−2=1.32×10−2M_{\text{total}} = 1.2 \times 10^{-3} + 1.2 \times 10^{-2} = 0.12 \times 10^{-2} + 1.2 \times 10^{-2} = 1.32 \times 10^{-2} grams
To add terms in scientific notation, convert them to have matching exponents before adding coefficients.

Key Concept

Arithmetic operations with Scientific Notation and Decimals
Estimated Time:1m 30s
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Topics

Decimals and Scientific Notation

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