Final answer:
Numbers that are entered into a formula and do not change are known as exact numbers. These numbers have an infinite number of significant figures and do not limit the significant figures in the calculated answer, affecting precision only by the measured values in the formula.
Step-by-step explanation:
Numbers entered directly into a formula that do not change are called exact numbers. These are numbers that come from a defined relationship and they technically have an unlimited number of significant figures. For example, the prefix kilo- means 1,000, exactly, neither adding to nor restricting the significant figures in the final calculation. When we use exact numbers in mathematical operations such as multiplication or division, we do not alter the precision of the numerical answer.
It is important to understand that exact numbers, such as conversion factors (like 1,000 in kilo-), do not affect the determination of the number of significant figures in the final answer. This is because exact numbers can be considered to have an infinite number of significant figures; therefore, other numbers' precision in the formulas govern the accuracy.
When functions like sine, cosine, logarithms, or exponential functions appear in an equation, they require pure numbers as inputs, which means that dimensionless quantities or exact numbers are used within these functions. The output of these calculations remains as pure numbers, with the original exact number not limiting the precision of the result.