What is $4,500,000,000$ in scientific notation?
A. $45 \times 10^{-7}$
B. $4.5 \times 10^9$
C. $4.5 \times 10^{-9}$
D. $4.5 \times 10^8$
Answer (1)
Convert the number to the form a × 1 0 b , where 1 ≤ a < 10 .
Move the decimal point 9 places to the left to get 4.5 .
Multiply 4.5 by 1 0 9 to get 4.5 × 1 0 9 .
The answer is 4.5 × 1 0 9 .
Explanation
Understanding Scientific Notation We need to express the number 4 , 500 , 000 , 000 in scientific notation. Scientific notation is a way of writing numbers as a product of a number between 1 and 10 (including 1 but excluding 10) and a power of 10.
Moving the Decimal Point To convert 4 , 500 , 000 , 000 to scientific notation, we first identify the decimal point, which is at the end of the number. We then move the decimal point to the left until we have a number between 1 and 10. In this case, we move the decimal point 9 places to the left to get 4.5 .
Expressing in Scientific Notation Since we moved the decimal point 9 places to the left, we multiply 4.5 by 1 0 9 to get 4.5 × 1 0 9 . Therefore, 4 , 500 , 000 , 000 = 4.5 × 1 0 9 .
Identifying the Correct Option Comparing our result with the given choices, we see that 4.5 × 1 0 9 is one of the options.
Final Answer Thus, 4 , 500 , 000 , 000 in scientific notation is 4.5 × 1 0 9 .
Examples
Scientific notation is incredibly useful in fields like astronomy and physics, where dealing with extremely large or small numbers is common. For instance, the distance to a galaxy might be 4.5 x 10^25 meters, or the mass of an electron might be 9.1 x 10^-31 kilograms. Writing these numbers in scientific notation makes them easier to handle and compare, preventing errors from counting numerous zeros. It's also used in computer science to represent floating-point numbers and in chemistry to express concentrations of solutions.
