The U.S. population was about $321,400,000$ in 2015. What's this number in scientific notation?
A. $3.214 \times 10^7$
B. $3.214 \times 10^8$
C. $3.214 \times 10^9$
D. $321.4 \times 10^6$
Answer (1)
Express the number in the form a × 1 0 n , where 1 ≤ a < 10 .
Determine the value of a : a = 3.214 .
Count the number of places the decimal point must be moved to the left: 8 places.
Write the number in scientific notation: 3.214 × 1 0 8 .
Explanation
Understanding Scientific Notation We are given the U.S. population in 2015 as approximately 321 , 400 , 000 . Our goal is to express this number in scientific notation, which is a way of writing numbers as a product of a number between 1 and 10 and a power of 10.
Identifying the Base Number To convert 321 , 400 , 000 to scientific notation, we need to write it in the form a × 1 0 n , where 1 ≤ a < 10 and n is an integer. In this case, a = 3.214 .
Determining the Exponent Now, we need to find the exponent n . To do this, we count how many places we need to move the decimal point in 321 , 400 , 000 to the left to get 3.214 . Starting from 321 , 400 , 000.0 , we move the decimal point 8 places to the left to get 3.21400000 .
Expressing in Scientific Notation Therefore, 321 , 400 , 000 = 3.214 × 1 0 8 .
Selecting the Correct Option Comparing our result with the given options, we see that the correct answer is 3.214 × 1 0 8 .
Final Answer Thus, the U.S. population in 2015 in scientific notation is 3.214 × 1 0 8 .
Examples
Scientific notation is extremely useful in fields like astronomy, where distances between stars and galaxies are vast. For instance, the distance to the Andromeda Galaxy is approximately 2.5 million light-years, which can be written as 2.5 × 1 0 6 light-years. Similarly, in microbiology, the size of a bacterium might be 2 × 1 0 − 6 meters. Using scientific notation makes it easier to work with very large and very small numbers, simplifying calculations and comparisons.
