Select the best answer for the question.
9. What is the value of $12.5 \times 10^7$?
A. 12.5000000
B. $125,000,000$
C. $1,250,000$
D. 1.2500000
Answer (1)
We are asked to calculate 12.5 × 1 0 7 .
Rewrite 12.5 as 1.25 × 1 0 1 .
Calculate 1.25 × 1 0 1 × 1 0 7 = 1.25 × 1 0 8 .
Convert to standard notation: 1.25 × 1 0 8 = 125 , 000 , 000 . The answer is 125 , 000 , 000 .
Explanation
Understanding the Problem We are asked to find the value of 12.5 × 1 0 7 . This means we need to multiply 12.5 by 10 to the power of 7.
Rewriting the Expression To calculate 12.5 × 1 0 7 , we can rewrite 12.5 as 1.25 × 1 0 1 . Then we have: 12.5 × 1 0 7 = 1.25 × 1 0 1 × 1 0 7 = 1.25 × 1 0 1 + 7 = 1.25 × 1 0 8
Calculating the Value Now, we need to write 1.25 × 1 0 8 in standard notation. Since 1 0 8 = 100 , 000 , 000 , we have: 1.25 × 1 0 8 = 1.25 × 100 , 000 , 000 = 125 , 000 , 000
Selecting the Correct Answer Comparing the result with the given options, we see that the correct answer is 125 , 000 , 000 .
Examples
Understanding scientific notation is crucial in many real-world applications. For instance, scientists use it to express very large or very small numbers, such as the distance to stars or the size of atoms. In finance, large sums of money or market capitalization of companies are often expressed using scientific notation. For example, if a company's market cap is 1.25 × 1 0 8 dollars, it means the company is worth 125 , 000 , 000 dollars. This notation simplifies the representation and comprehension of such large values.
