The Correct Answer and Explanation is:
Correct Answer: 3050
Explanation
The problem asks to convert the number 3.05 x 10^3 from scientific notation to standard form. Standard form is the conventional way we write numbers in everyday life, for example, 12, 450, or 0.75. Scientific notation, on the other hand, is a method used to express very large or very small numbers in a compact and consistent format. It is written as a product of a number between 1 and 10 (the coefficient) and a power of 10.
In the given expression, 3.05 is the coefficient, and 10^3 is the power of ten. The exponent, which is 3 in this case, is the key to the conversion. A positive exponent indicates that we are dealing with a number greater than 10. The value of the exponent tells us how many times to multiply the coefficient by 10.
So, 10^3 is equivalent to 10 multiplied by itself three times:
10^3 = 10 × 10 × 10 = 1000.
Now, we can rewrite the original expression as a simple multiplication problem:
3.05 × 1000
Multiplying 3.05 by 1000 gives us 3050.
An alternative and often quicker method for this conversion involves moving the decimal point. The exponent, 3, tells us to move the decimal point three places to the right. We move to the right because the exponent is positive, which makes the number larger.
Let’s trace the movement of the decimal point in 3.05:
- Starting with 3.05, the first move to the right gives us 30.5.
- The second move to the right gives us 305.
- For the third and final move, there are no more digits. We must add a zero as a placeholder to complete the move. This gives us 3050.
Both methods yield the same result. Therefore, the number 3.05 x 10^3 written in standard form is 3050.
