How do you write 0.00001 in scientific notation?
The Correct Answer and Explanation is:
Correct Answer:
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 compact and manageable form. This method is especially useful in science, engineering, and mathematics where such numbers frequently appear.
To write a number in scientific notation, the number must be expressed as the product of two factors: a decimal number between 1 and 10, and a power of 10. The general format is:
a × 10ⁿ
Here, a is a number that is greater than or equal to 1 and less than 10, and n is an integer that represents how many places the decimal point must be moved to convert the original number into a.
Let’s apply this to 0.00001.
First, identify the significant digits in the number. In this case, the only significant digit is 1. To convert this into a number between 1 and 10, we write it as 1.0 (or just 1).
Next, determine how many decimal places we need to move the point to the right in order to get from 1 to the original number 0.00001. Starting from 1.0, we move the decimal five places to the left to get 0.00001. Because we are moving the decimal to the left, the exponent of 10 is negative. Therefore, the exponent is -5.
Putting it all together, we get:
0.00001 = 1 × 10⁻⁵
This notation helps reduce errors in calculation and simplifies writing. For example, in scientific work, writing 0.0000000000034 can be difficult and time-consuming. Instead, writing 3.4 × 10⁻¹² is faster and clearer. Scientific notation also makes it easier to compare the sizes of very small or very large numbers quickly just by looking at the exponent.
So, 0.00001 in scientific notation is written as 1 × 10⁻⁵.
