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Difficulty: MediumScientific Notation

An experimental particle travels a distance of 4.5×1054.5 \times 10^5 meters in 5.0×10−35.0 \times 10^{-3} seconds. What is the average speed of the particle in meters per second, expressed in proper scientific notation?

  1. 9.0×1079.0 \times 10^7Answer
  2. B
    9.0×1019.0 \times 10^1
  3. C
    9.0×1099.0 \times 10^9
  4. D
    9.0×1089.0 \times 10^8

Answer

The correct speed is 9.0×1079.0 \times 10^7 meters per second.
To divide numbers in scientific notation, divide the coefficients and subtract the exponents. Dividing 4.54.5 by 5.05.0 yields 0.90.9. Subtracting the exponent −3-3 from 55 yields 88 (since 5−(−3)=5+3=85 - (-3) = 5 + 3 = 8). This gives an intermediate result of 0.9×1080.9 \times 10^8. To convert this into proper scientific notation, the coefficient must be between 11 and 1010. Moving the decimal point one place to the right converts 0.90.9 to 9.09.0, which requires decreasing the exponent by 11, resulting in the final correct answer of 9.0×1079.0 \times 10^7.

Step-by-Step Solution

1
Divide the coefficients given in the problem: 4.5÷5.04.5 \div 5.0.
0.90.9
When dividing numbers in scientific notation, the coefficients are divided separately from the powers of 10.
2
Divide the powers of 10 by subtracting the denominator's exponent from the numerator's exponent: 105÷10−310^5 \div 10^{-3}.
105−(−3)=10810^{5 - (-3)} = 10^8
According to the laws of exponents, division of like bases requires subtracting the exponent of the divisor from the exponent of the dividend.
3
Combine the newly calculated coefficient and power of 10.
0.9×1080.9 \times 10^8
This represents the mathematical result before applying proper formatting rules.
4
Normalize the answer by moving the decimal point one place to the right to make the coefficient between 1 and 10, and subtract 1 from the exponent to balance the shift.
9.0×1079.0 \times 10^7
Proper scientific notation requires the coefficient to be greater than or equal to 1 and less than 10.

Key Concept

Scientific Notation Division and Normalization
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Topics

Scientific Notation

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