Examkin

Question

Difficulty: MediumScientific Notation

A biomedical researcher is cataloging the diameters of four microscopic specimens. To properly calibrate the imaging equipment, arrange the specimens in descending order based on their diameter, from the largest to the smallest.

  1. 1Specimen Beta: 0.0000720.000072 meters
  2. 2Specimen Delta: 0.9×10−50.9 \times 10^{-5} meters
  3. 3Specimen Gamma: 850×10−8850 \times 10^{-8} meters
  4. 4Specimen Alpha: 6.5×10−66.5 \times 10^{-6} meters

Answer

The correct descending order from largest to smallest is Specimen Beta, Specimen Delta, Specimen Gamma, and Specimen Alpha.
By converting all measurements into standard scientific notation (a×10na \times 10^n), their magnitudes can be compared directly. Specimen Beta has the largest exponent (−5-5). The remaining three specimens all reduce to an exponent of −6-6. Ordering those three by their coefficients (9.09.0, 8.58.5, and 6.56.5) yields the final sequence.

Step-by-Step Solution

1
Convert Specimen Beta from standard decimal form to scientific notation.
0.0000720.000072 meters becomes 7.2×10−57.2 \times 10^{-5} meters.
A uniform mathematical format is necessary to accurately compare the magnitudes of all specimens.
2
Normalize the coefficient for Specimen Gamma.
850×10−8850 \times 10^{-8} becomes 8.5×10−68.5 \times 10^{-6}.
Proper scientific notation requires the coefficient to be greater than or equal to 1 and less than 10. Moving the decimal two places left increases the exponent by 2.
3
Normalize the coefficient for Specimen Delta.
0.9×10−50.9 \times 10^{-5} becomes 9.0×10−69.0 \times 10^{-6}.
Moving the decimal one place right to create a valid coefficient decreases the exponent by 1.
4
Compare the exponents first, then the coefficients to determine the descending order.
7.2×10−5>9.0×10−6>8.5×10−6>6.5×10−67.2 \times 10^{-5} > 9.0 \times 10^{-6} > 8.5 \times 10^{-6} > 6.5 \times 10^{-6}.
A larger exponent (−5-5 vs −6-6) dictates a larger overall number. For values sharing the identical −6-6 exponent, the descending order is determined directly by their coefficients (9.0>8.5>6.59.0 > 8.5 > 6.5).

Key Concept

Normalizing Coefficients and Comparing Magnitudes in Scientific Notation
Estimated Time:1m 30s
Rate this question

Topics

Scientific Notation

More questions from this topic