Examkin

Question

Difficulty: MediumExponents, 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 10^6Answer
  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

Answer

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.

Step-by-Step Solution

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.

Key Concept

Division of numbers expressed in scientific notation
Rate this question

Topics

Exponents, Roots, and Scientific Notation

More questions from this topic