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Zorluk: OrtaExponents, Roots, and Scientific Notation

A high-speed fiber-optic cable transmits data at a rate of 8.0×1078.0 \times 10^7 bytes per second. A digital archive containing a total of 3.2×10113.2 \times 10^{11} bytes needs to be transmitted. How many seconds will it take to complete the transmission?

  1. A
    2.5×10−42.5 \times 10^{-4}
  2. B
    4.0×1044.0 \times 10^4
  3. 4.0×1034.0 \times 10^3Cevap
  4. D
    4.0×10174.0 \times 10^{17}
  5. E
    2.56×10192.56 \times 10^{19}

Cevap

The transmission will take 4.0×1034.0 \times 10^3 seconds.
The correct answer represents the transmission time of 4.0×1034.0 \times 10^3 seconds. This is determined by dividing the total data volume, 3.2×10113.2 \times 10^{11} bytes, by the rate, 8.0×1078.0 \times 10^7 bytes per second. The division yields 3.28.0×1011−7=0.4×104\frac{3.2}{8.0} \times 10^{11 - 7} = 0.4 \times 10^4. Converting this value to standard scientific notation by moving the decimal point one digit to the right reduces the power of 1010 by one, resulting in 4.0×1034.0 \times 10^3.

Adım Adım Çözüm

1
Set up the division to find the transmission time.
Time=3.2×1011 bytes8.0×107 bytes/second\text{Time} = \frac{3.2 \times 10^{11}\text{ bytes}}{8.0 \times 10^7\text{ bytes/second}}
To find the total time, divide the total quantity of data by the transmission rate.
2
Divide the numerical coefficients.
3.28.0=0.4\frac{3.2}{8.0} = 0.4
When dividing numbers written in scientific notation, divide the coefficients first.
3
Apply the quotient rule of exponents to the powers of 10.
1011107=1011−7=104\frac{10^{11}}{10^7} = 10^{11 - 7} = 10^4
Subtract the exponent in the denominator from the exponent in the numerator.
4
Combine the intermediate parts and convert to standard scientific notation.
0.4×104=4.0×1030.4 \times 10^4 = 4.0 \times 10^3
Standard scientific notation requires the coefficient to be at least 1 but strictly less than 10. Shifting the decimal point one place to the right decreases the exponent by 1.

Anahtar Kavram

Dividing numbers in scientific notation and converting to standard form
Tahmini Süre:1m 0s
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Exponents, Roots, and Scientific Notation

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