Final answer:
The smallest normalized number in the specified decimal system with 6 decimal digits for the significand is 1.00000 x 10^-99. One must understand the principles of scientific notation and significant figures to determine this. It involves adjusting the decimal place until the value has a coefficient between 1 and 10.
Step-by-step explanation:
The question asks about the smallest normalized number in a decimal system that provides 6 decimal digits for the significand. By definition, the smallest normalized number in any base system uses 1 as the first digit of the significand and the exponent chosen is the smallest possible for the system.
Thus, the smallest normalized number would be 1.00000 x 10^-99 (Option a). The other options present different exponent values, but based on the criteria for the smallest normalized number in the mentioned decimal system, option a is the correct answer. It is important to have a solid understanding of scientific notation and significant figures to properly comprehend these concepts.
To further illustrate the process, converting ordinary numbers to scientific notation involves either moving the decimal to the right or left side until you obtain a coefficient that is between 1 and 10 followed by a power of 10 that reflects the number of places the decimal has been moved. Regarding the number of significant figures, any non-zero digit or zeros between significant digits are always significant. The zeros used to position the decimal point in a number are significant only if they have been measured or are known precisely. In scientific notation, the exponent does not contribute to the number of significant figures, as it represents the order of magnitude rather than measured values.