write your answer in scientific notation:
0.0006 × 5,000,000
The correct answer and explanation is:
To express the product of 0.0006×5,000,0000.0006 \times 5,000,000 in scientific notation, we first calculate the product: 0.0006×5,000,000=3,0000.0006 \times 5,000,000 = 3,000
Now, to express 3,000 in scientific notation, we need to write it as a number between 1 and 10, multiplied by a power of 10. The number 3,000 can be written as: 3,000=3×1033,000 = 3 \times 10^3
Thus, the result of 0.0006×5,000,0000.0006 \times 5,000,000 in scientific notation is: 3×1033 \times 10^3
Explanation:
Scientific notation is a way of expressing very large or very small numbers in a more compact form. It is based on powers of 10, where a number is expressed as a product of a coefficient and a power of 10. The coefficient is usually a number between 1 and 10, and the power of 10 shows how many times the coefficient must be multiplied or divided by 10 to reach the original value.
In this case, when multiplying 0.00060.0006 by 5,000,0005,000,000, we first perform the multiplication to get 3,000. To express 3,000 in scientific notation, we look for the number of places we need to move the decimal point to transform 3,000 into a number between 1 and 10. Moving the decimal point three places to the left gives us 3. Therefore, the power of 10 is 3, indicating that 3,000 is equal to 3×1033 \times 10^3.
This method of writing numbers is useful for simplifying calculations and for working with very large or very small numbers in fields like science and engineering.