What is 5.2×10^4 in standard form
The Correct Answer and Explanation is :
The correct answer is: 52000
To convert ( 5.2 \times 10^4 ) into standard form, we follow the rules of scientific notation. In scientific notation, a number is expressed as the product of a coefficient (a number greater than or equal to 1 and less than 10) and a power of 10.
Step 1: Understanding Scientific Notation
In this case, ( 5.2 ) is the coefficient, and ( 10^4 ) indicates that we will be moving the decimal point in ( 5.2 ) four places to the right. This movement is determined by the exponent of 10. Since the exponent is positive, it signifies that the number is greater than 1.
Step 2: Moving the Decimal Point
Starting with ( 5.2 ):
- The decimal point is initially at the end of the number: ( 5.2. )
- Moving it four places to the right means we will add zeros as placeholders for each space we move past the existing digits.
- Move 1: ( 5.2 \rightarrow 52. )
- Move 2: ( 52 \rightarrow 520. )
- Move 3: ( 520 \rightarrow 5200. )
- Move 4: ( 5200 \rightarrow 52000. )
After moving the decimal point four places to the right, we have ( 52000 ).
Step 3: Writing in Standard Form
Thus, ( 5.2 \times 10^4 ) in standard form is:
[
52000
]
Summary
The standard form of ( 5.2 \times 10^4 ) is ( 52000 ). This process illustrates how scientific notation allows for easier handling of large numbers by providing a compact representation. The key takeaway is that the exponent indicates how many places to move the decimal point, which helps in converting back and forth between scientific and standard forms efficiently. Understanding this conversion is crucial, especially in fields like science and engineering, where large numbers are frequently used.