What is 0.000678 written in scientific notation?
A. $6.78 \times 10^{-3}$
B. $6.78 \times 10^{-5}$
C. $6.78 \times 10^{-4}$
D. $678 \times 10^6$
Answer (1)
Move the decimal point in 0.000678 four places to the right to obtain 6.78.
Multiply 6.78 by 1 0 − 4 to represent the original number.
Express 0.000678 in scientific notation as 6.78 × 1 0 − 4 .
The final answer is 6.78 × 1 0 − 4 .
Explanation
Understanding the Problem We need to express the number 0.000678 in scientific notation. Scientific notation is a way of writing numbers as a product of a number between 1 and 10 (including 1) and a power of 10.
Moving the Decimal Point To convert 0.000678 to scientific notation, we need to move the decimal point until we have a number between 1 and 10.
Finding the Correct Number Move the decimal point 4 places to the right: 0.000678 becomes 6.78.
Determining the Exponent Since we moved the decimal point 4 places to the right, we multiply 6.78 by 1 0 − 4 to get the original number.
Final Answer Therefore, 0.000678 in scientific notation is 6.78 × 1 0 − 4 .
Examples
Scientific notation is useful in many real-world scenarios, especially when dealing with very large or very small numbers. For example, in astronomy, the distance to a star might be 4.3 light-years, which is approximately 40,680,000,000,000 kilometers. Writing this in scientific notation as 4.068 × 1 0 13 km makes it much easier to handle. Similarly, in biology, the size of a bacterium might be 0.000002 meters, which is more conveniently written as 2 × 1 0 − 6 meters. Scientific notation simplifies calculations and comparisons involving such extreme values.
