The correct range of numbers for the first part of scientific notation is 1 to 10 (option a). This ensures that the coefficient is between 1 (inclusive) and 10 (exclusive), which is a principle of scientific notation for ease of computation with very large or very small numbers.
The range of numbers that can be used in correctly writing the first part of scientific notation is 1 to 10. In scientific notation, a number is expressed as N x 10^n, where N (the coefficient) is a number greater than or equal to 1 but less than 10. For example, to write the number 637.8 in scientific notation, you would write it as 6.378 x 10² because the coefficient is now in the range from 1 up to 10 and the exponent shows how many places the decimal point has moved.
Correct scientific notation ensures that the coefficient is a number that maintains this range, which makes computations with very large or very small numbers manageable. Numerical expressions like 345.1 x 10² need to be adjusted to meet the scientific notation criteria. For instance, 345.1 x 10² would be rewritten as 3.451 x 10⁴. The rule is consistently applied in all cases, whether dealing with positive or negative exponents.
Therefore, the correct answer to the question is a. 1 to 10, which fits the definition and proper expression of scientific notation.