Please give me the correct answer. Scientific Notation Tutorial Part 1 Level A skin cell is between 0.00003 and 0.00004 meters thick. How do you write 0.00003 in scientific notation? If we start with 3 and shift it to the right 5 times to get 0.00003, should we represent this as 3 x 10^5 or 3 x 10^-5? 0.00003 = 3 x 10^2 3 x 10^5 3 x 10^-5
The Correct Answer and Explanation is:
The correct scientific notation for 0.00003 is 3 × 10⁻⁵.
Here’s why.
Scientific notation is a way to write very large or very small numbers using powers of ten. It expresses a number in the form a × 10ⁿ, where a is a number between 1 and 10, and n is an integer that tells us how many places to move the decimal point.
To write 0.00003 in scientific notation, we first identify the significant digits: here, that’s 3. We then determine how many places we must move the decimal point to convert 0.00003 into 3. The decimal needs to shift five places to the right. Since we are making a small number larger, the exponent of ten must be negative, indicating a number much less than 1.
So we write:
0.00003 = 3 × 10⁻⁵
The negative exponent tells us that the decimal point in 3 × 10⁻⁵ has moved five places to the left to reach 0.00003.
To confirm:
- 10⁻¹ = 0.1
- 10⁻² = 0.01
- 10⁻³ = 0.001
- 10⁻⁴ = 0.0001
- 10⁻⁵ = 0.00001
Then: 3 × 0.00001 = 0.00003
That verifies the conversion is accurate.
The other options are incorrect:
- 3 × 10² = 300
- 3 × 10⁵ = 300000
These represent numbers far larger than the width of a skin cell.
Scientific notation is commonly used in science and engineering where extremely small or large values are frequent. It makes reading, comparing, and calculating these quantities much more manageable.
