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Zorluk: OrtaExponents, Roots, and Scientific Notation

A microchip manufacturer produces 2.4×1082.4 \times 10^8 components per day across 4 identical production lines. Each line operates for 20 hours per day. On average, how many components are produced per hour on a single production line?

  1. A
    3.0×1053.0 \times 10^5
  2. 3.0×1063.0 \times 10^6Cevap
  3. C
    1.2×1071.2 \times 10^7
  4. D
    3.0×1073.0 \times 10^7
  5. E
    4.8×1094.8 \times 10^9

Cevap

3.0×1063.0 \times 10^6 components per hour
To find the hourly output of a single line, first divide the total components (2.4×1082.4 \times 10^8) by the 4 lines to get 6.0×1076.0 \times 10^7 components per line per day. Then, divide by the 20 operating hours (2.0×1012.0 \times 10^1) to obtain 3.0×1063.0 \times 10^6 components per hour per line.

Adım Adım Çözüm

1
Calculate daily production per single line
2.4×1084=0.6×108=6.0×107\frac{2.4 \times 10^8}{4} = 0.6 \times 10^8 = 6.0 \times 10^7 components per line per day
The total daily output is split equally among 4 identical lines.
2
Calculate hourly production per single line
6.0×10720=6.0×1072.0×101=3.0×106\frac{6.0 \times 10^7}{20} = \frac{6.0 \times 10^7}{2.0 \times 10^1} = 3.0 \times 10^6 components per hour
Dividing daily output per line by the 20 operating hours per day gives the hourly rate per line.

Anahtar Kavram

Division of numbers expressed in scientific notation
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Konular

Exponents, Roots, and Scientific Notation

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