The Correct Answer and Explanation is:
Correct Answer: 600,000,000
The problem shown in the image is the multiplication of 300,000 by 2,000. The correct answer is 600,000,000, which is six hundred million.
There is a straightforward method for solving multiplication problems that involve large numbers ending in multiple zeros. This approach simplifies the calculation by breaking it into two manageable parts.
First, you can ignore the zeros and multiply only the significant, non-zero digits from each number. In this specific problem, the significant digits are 3 and 2. The multiplication of these two numbers is quite simple: 3 times 2 equals 6. This number will form the beginning of our final answer.
Second, you need to count the total number of zeros from both of the original numbers. The number 300,000 has five zeros. The number 2,000 has three zeros. To find the total number of zeros for the final product, you add the counts together. So, 5 zeros plus 3 zeros gives a total of 8 zeros.
Finally, you combine the results from the first and second steps. You take the product of the significant digits, which was 6, and then you attach the total number of zeros you counted, which was eight. Placing eight zeros after the 6 gives you the final result: 600,000,000.
This technique is a practical application of mathematical principles involving powers of ten. The number 300,000 can be written in scientific notation as 3 × 10^5, and 2,000 can be written as 2 × 10^3. When you multiply these, you multiply the coefficients (3 × 2 = 6) and add the exponents of ten (5 + 3 = 8), resulting in 6 × 10^8. This is the scientific notation for 600,000,000, confirming the answer is correct.
