Final answer:
To find the smallest power of 10 greater than M, calculate the common logarithm of M to base 10, and round up to the next integer. The resulting power of 10 will be the smallest power that exceeds M.
Step-by-step explanation:
To find the smallest power of 10 that exceeds a given positive integer M, you would use logarithms. Specifically, by finding the common logarithm of M to the base 10, which is the power to which 10 must be raised to equal M. Once the logarithm is found, you round it up to the nearest whole number, because you want the next largest power of 10 that exceeds M. So if M's logarithm is a non-integer, the next integer is the smallest power. If, however, the logarithm is an integer, you must add 1 to find the next power.
Correct Option: C. Find the logarithm of M to the base 10 and then round up to the next integer. This will give you the smallest power of 10 greater than M.
For example:
If M = 150, the common logarithm of 150 is approximately 2.18. Rounding up gives us 3, meaning that 103 or 1,000, is the smallest power of 10 that exceeds 150.