What is 0.000678 written in scientific notation?
A. $6.78 \times 10^{-3}$
B. $678 \times 10^6$
C. $6.78 \times 10^{-5}$
D. $6.78 \times 10^{-4}$
Answer (2)
Convert 0.000678 into scientific notation.
Move the decimal point four places to the right to obtain 6.78.
Determine the exponent as -4 since the decimal was moved four places to the right.
Express the result in scientific notation: 6.78 × 1 0 − 4 .
Explanation
Understanding Scientific Notation We need to express the number 0.000678 in scientific notation. Scientific notation requires us to write the number in the form a × 1 0 b , where 1 ≤ a < 10 and b is an integer.
Moving the Decimal Point To convert 0.000678 to scientific notation, we need to move the decimal point to the right until we have a number between 1 and 10. Moving the decimal point four places to the right gives us 6.78, which satisfies the condition 1 ≤ a < 10 .
Determining the Exponent Since we moved the decimal point four places to the right, the exponent b will be -4. This is because we are effectively dividing 0.000678 by 1 0 − 4 to get 6.78.
Final Scientific Notation Therefore, 0.000678 in scientific notation is 6.78 × 1 0 − 4 .
Final Answer The correct answer is 6.78 × 1 0 − 4 .
Examples
Scientific notation is incredibly useful in fields like astronomy and chemistry. For example, the distance to a nearby star might be 4.017 x 10^16 meters, and the mass of a hydrogen atom is approximately 1.67 x 10^-27 kilograms. These notations make handling very large or very small numbers much more manageable.
The number 0.000678 in scientific notation is expressed as 6.78 × 1 0 − 4 . This is achieved by moving the decimal point four places to the right and indicating a negative exponent. Thus, the correct choice is D.
;
