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Zorluk: KolayScientific Notation and Unit Conversions

During a biology experiment, a student measures the lengths of four different biological specimens. Based on these measurements, arrange the following specimens in order from smallest to largest length.

  1. 1Virus (40 nm40\text{ nm})
  2. 2Bacterium (2.0 μm2.0\text{ }\mu\text{m})
  3. 3Red blood cell (8.0 μm8.0\text{ }\mu\text{m})
  4. 4Human hair diameter (0.1 mm0.1\text{ mm})

Cevap

Virus (40 nm40\text{ nm}), Bacterium (2.0 μm2.0\text{ }\mu\text{m}), Red blood cell (8.0 μm8.0\text{ }\mu\text{m}), Human hair diameter (0.1 mm0.1\text{ mm})
To arrange the specimens from smallest to largest, convert each value to meters using standard scientific notation. The prefix nano- represents 10−910^{-9}, micro- represents 10−610^{-6}, and milli- represents 10−310^{-3}. Converting the values yields: Virus = 4.0×10−8 m4.0 \times 10^{-8}\text{ m}, Bacterium = 2.0×10−6 m2.0 \times 10^{-6}\text{ m}, Red blood cell = 8.0×10−6 m8.0 \times 10^{-6}\text{ m}, and Human hair = 1.0×10−4 m1.0 \times 10^{-4}\text{ m}. Comparing the exponents shows that the virus is the smallest, followed by the bacterium and the red blood cell (since both have an exponent of −6-6 and 2.0<8.02.0 < 8.0), and the human hair is the largest.

Adım Adım Çözüm

1
Convert all measurements to a common unit, meters (m\text{m}), using scientific notation.
Virus: 40 nm=40×10−9 m=4.0×10−8 m40\text{ nm} = 40 \times 10^{-9}\text{ m} = 4.0 \times 10^{-8}\text{ m}. Bacterium: 2.0 μm=2.0×10−6 m2.0\text{ }\mu\text{m} = 2.0 \times 10^{-6}\text{ m}. Red blood cell: 8.0 μm=8.0×10−6 m8.0\text{ }\mu\text{m} = 8.0 \times 10^{-6}\text{ m}. Human hair: 0.1 mm=0.1×10−3 m=1.0×10−4 m0.1\text{ mm} = 0.1 \times 10^{-3}\text{ m} = 1.0 \times 10^{-4}\text{ m}.
To compare physical sizes, they must be represented in the same base unit and format.
2
Compare the exponents of the values in scientific notation.
The exponents are −8-8 for the virus, −6-6 for both the bacterium and the red blood cell, and −4-4 for the human hair.
A smaller (more negative) exponent in scientific notation indicates a smaller value.
3
Compare values with the same exponent and arrange the entire list from smallest to largest.
Comparing the coefficients for the exponent −6-6: 2.0<8.02.0 < 8.0. Therefore, 2.0×10−6 m2.0 \times 10^{-6}\text{ m} is smaller than 8.0×10−6 m8.0 \times 10^{-6}\text{ m}. The final ordered list is: Virus, Bacterium, Red blood cell, and Human hair.
For values with the same exponent, compare their coefficients directly.

Anahtar Kavram

Converting metric units to scientific notation in base meters and comparing exponent values.
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Konular

Scientific Notation and Unit Conversions

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