Write each number in scientific notation. 0.0027
The correct answer and explanation is:
Correct Answer:
0.0027 in scientific notation is 2.7 × 10⁻³
Explanation:
Scientific notation is a method used to express very large or very small numbers in a more compact and manageable form. It is written in the form:
a × 10ⁿ,
where a is a number greater than or equal to 1 but less than 10, and n is an integer.
To convert 0.0027 into scientific notation, start by identifying where the decimal point needs to move in order to make the number between 1 and 10. The number 0.0027 is smaller than 1, so the decimal point needs to be moved to the right.
Moving the decimal point three places to the right gives:
2.7
Each movement of the decimal point to the right corresponds to a decrease in power of 10 by 1. Therefore, since the decimal point was moved three places, the exponent will be -3. The negative sign shows that the original number is less than 1.
So, 0.0027 becomes:
2.7 × 10⁻³
This tells that the number is 2.7 divided by 1,000, which gives back the original value of 0.0027.
Scientific notation is useful in scientific and mathematical contexts because it simplifies calculations involving extremely large or small numbers. For example, numbers like 0.00000056 or 450000000 can be rewritten as 5.6 × 10⁻⁷ or 4.5 × 10⁸ respectively, making them easier to read and work with. This format is especially common in disciplines such as physics, chemistry, and astronomy where such values occur frequently.