How do you write 0.00001 in scientific notation?
The Correct Answer and Explanation is:
Scientific Notation of 0.00001
The number 0.00001 in scientific notation is written as:
1 × 10⁻⁵
Explanation
Scientific notation is a way of expressing very large or very small numbers in a more compact and manageable form. It is commonly used in science, engineering, and mathematics to simplify calculations and clearly indicate the scale of a number. The general format of scientific notation is:
a × 10ⁿ
Here, a is a number greater than or equal to 1 and less than 10. The exponent n is an integer that shows how many times the decimal point must be moved to convert the number back to its standard form.
To convert 0.00001 into scientific notation, follow these steps:
- Identify the significant digits: The only non-zero digit in 0.00001 is 1.
- Place the decimal point after the significant digit: This gives us 1.0.
- Count how many places the decimal point must move to the right to return to the original number: In this case, the decimal point moves 5 places to the left to go from 1.0 to 0.00001.
- Use a negative exponent: Since the decimal point moves to the left, the exponent on 10 is negative.
So, 0.00001 = 1.0 × 10⁻⁵
This tells us that 1.0 needs to be divided by 100000 (which is 10 raised to the power of 5) to get back to 0.00001. The negative exponent reflects that the original number is less than 1.
Using scientific notation makes it easier to write very small numbers like this without needing to write out all the zeros. It also simplifies mathematical operations such as multiplication and division. Scientists and engineers rely on this notation to communicate measurements and calculations clearly, especially when dealing with extremely small or large quantities.
