Consider this number in scientific notation.

Question

3.75 × 108

Which is true about writing the number in standard form? Check all that apply.
Move the decimal point eight places to the left.
This will convert to a very large number.
Move the decimal point ten places to the right.
This will convert to a very small number.
This is the same as the product of 3.75 and 100,000,000.

Answer 1

To analyze the scientific notation \(3.75 \times 10^8\), let's evaluate the statements one by one:

1. Move the decimal point eight places to the left.

   • False: To convert from scientific notation to standard form, you move the decimal point to the right for positive exponents.

2. This will convert to a very large number.

   • True: The number \(3.75 \times 10^8\) corresponds to \(375,000,000\), which is indeed a very large number.

3. Move the decimal point ten places to the right.

   • False: You only need to move the decimal point eight places to the right, not ten.

4. This will convert to a very small number.

   • False: The number is large; hence, it does not convert to a small number.

5. This is the same as the product of 3.75 and 100,000,000.

   • True: This statement is accurate because \(3.75 \times 10^8\) is indeed the same as multiplying \(3.75\) by \(100,000,000\) (which is \(10^8\)).

Based on this analysis, the true statements are:

• This will convert to a very large number.
• This is the same as the product of 3.75 and 100,000,000.