Select the best answer for the question.
According to the Wall Street Journal, $14,200,000$ copies of Walt Disney's Fantasia have been sold to date. Write that number in scientific notation.
A. $1.42=10^7$
B. $142 \times 10^7$
C. $142 \times 1,000,000$
D. $142 \times 10^{\circ}$
Answer (1)
Convert the number to scientific notation: 14 , 200 , 000 = 1.42 × 1 0 7 .
Compare the result with the given options.
Identify the closest option, interpreting the equals sign as multiplication.
The best answer is 1.42 × 1 0 7 .
Explanation
Understanding Scientific Notation We are asked to express the number 14,200,000 in scientific notation and choose the correct option from the given choices. Scientific notation is a way of writing numbers as a product of a number between 1 and 10 and a power of 10.
Converting to Scientific Notation To convert 14,200,000 to scientific notation, we need to move the decimal point to the left until we have a number between 1 and 10. In this case, we move the decimal point 7 places to the left to get 1.42.
Expressing in Scientific Notation Since we moved the decimal point 7 places to the left, we multiply 1.42 by 1 0 7 to get 1.42 × 1 0 7 .
Comparing with Options Now, we compare our result with the given options: A. 1.42 = 1 0 7 (Incorrect, as it's an equation, not scientific notation) B. 142 × 1 0 7 (Incorrect, as 142 is not between 1 and 10) C. 142 × 1 , 000 , 000 (Incorrect, as it's not in scientific notation) D. 142 × 1 0 ∘ (Incorrect, as it's not in scientific notation and 1 0 ∘ is unusual notation) However, option A is closest to the correct answer if we interpret the equals sign as "times".
Selecting the Best Answer The correct scientific notation for 14,200,000 is 1.42 × 1 0 7 . Although none of the options are perfectly written, option A, 1.42 = 1 0 7 , is the closest if we interpret the equals sign as a multiplication sign.
Examples
Scientific notation is useful in many real-world scenarios, especially when dealing with very large or very small numbers. For instance, astronomers use scientific notation to express distances between stars, like the distance to Proxima Centauri, which is approximately 4.017 × 1 0 13 kilometers. Similarly, biologists use it to describe the size of cells or bacteria, such as the size of an E. coli bacterium, which is about 2 × 1 0 − 6 meters. Using scientific notation makes these numbers easier to handle and compare.
