Determine the quotient. Write your answer in scientific notation.
$\left(26.4 \times 10^{-3}\right) \div\left(13.2 \times 10^4\right)$
Answer (2)
Divide the coefficients: 26.4 ÷ 13.2 = 2 .
Divide the powers of 10: 1 0 − 3 ÷ 1 0 4 = 1 0 − 7 .
Combine the results: 2 × 1 0 − 7 .
The quotient in scientific notation is 2 × 1 0 − 7 .
Explanation
Understanding the problem We are asked to determine the quotient of ( 26.4 × 1 0 − 3 ) ÷ ( 13.2 × 1 0 4 ) and express the result in scientific notation. Scientific notation requires the number to be in the form a × 1 0 b , where 1 ≤ ∣ a ∣ < 10 and b is an integer.
Dividing the coefficients To find the quotient, we divide the coefficients and the powers of 10 separately. First, divide the coefficients: 26.4 ÷ 13.2 = 2
Dividing the powers of 10 Next, divide the powers of 10: 1 0 4 1 0 − 3 = 1 0 − 3 − 4 = 1 0 − 7
Combining the results Now, combine the results: 2 × 1 0 − 7 This is already in scientific notation since 1 ≤ 2 < 10 .
Final Answer Therefore, the quotient is 2 × 1 0 − 7 .
Examples
Scientific notation is extremely useful in fields like physics and astronomy, where you often deal with very large or very small numbers. For example, the speed of light is approximately 3 × 1 0 8 meters per second, and the mass of an electron is approximately 9.11 × 1 0 − 31 kilograms. Using scientific notation makes these numbers easier to work with and understand.
The quotient of ( 26.4 × 1 0 − 3 ) ÷ ( 13.2 × 1 0 4 ) is 2 × 1 0 − 7 . This is determined by dividing the coefficients and subtracting the exponents of the powers of ten. The final result is expressed in scientific notation.
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