How do you write this in scientific notation?
52 thousandths
The Correct Answer and Explanation is :
Scientific Notation of 52 Thousandths
The value of 52 thousandths is ( 0.052 ). To express this in scientific notation, follow these steps:
- Identify the decimal form: The number is ( 0.052 ).
- Move the decimal point: In scientific notation, we represent numbers as ( a \times 10^n ), where ( a ) is a number between 1 and 10, and ( n ) is an integer. For ( 0.052 ), the decimal needs to be moved two places to the right to give a value between 1 and 10: ( 5.2 ).
- Adjust the exponent: Since the decimal point was moved two places to the right, the exponent will be negative. Thus, ( 0.052 ) becomes ( 5.2 \times 10^{-2} ).
Therefore, ( 0.052 ) in scientific notation is written as:
[
5.2 \times 10^{-2}
]
Explanation
Scientific notation is a method used to express very large or very small numbers in a concise and standardized form. It simplifies working with such numbers in mathematics, science, and engineering. The number is expressed as ( a \times 10^n ), where:
- ( a ) is a coefficient between 1 and 10.
- ( n ) is an integer, which indicates how many places the decimal point has been moved.
In the case of ( 0.052 ), the number is less than 1, so the decimal point needs to be shifted to the right to make the coefficient ( 5.2 ). Since moving the decimal right indicates a fraction (less than 1), the exponent is negative, showing how many places the decimal was shifted.
Scientific notation allows for easier calculations, particularly when multiplying or dividing large or small numbers, because the powers of 10 can be handled algebraically while the coefficients are manipulated separately.