Final answer:
A terminating decimal is one that has a finite number of digits after the decimal point, like 0.75. Significant figures are crucial when recording measurements to reflect the precision accurately, and calculators may give digits that are not significant. For whole numbers, scientific notation can clarify significant trailing zeros.
Step-by-step explanation:
An example of a terminating decimal is 0.75. This is a terminating decimal because it has a finite number of digits after the decimal point. We can tell it is terminating because 0.75 can be expressed as the fraction ⅔, which has a denominator of 4. Since 4 is a power of 2 (a factor of 2 squared), any fraction with a denominator that is a power of 2, or a power of 5, or a combination of both (such as 10, 20, 25, etc.), will result in a terminating decimal when expressed in decimal form.
When calculating and recording measurements, it is important to be mindful of the number of significant figures. These are the digits that carry meaning contributing to its precision. This includes all non-zero digits, any zeros between them, and trailing zeros in a number with a decimal point. Calculators may produce more digits than are significant, leading to false precision. Therefore, it is essential to round your calculated results to the appropriate number of significant figures to accurately reflect the precision of the measurements involved. Understanding significant figures is essential to ensure accurate reporting of scientific data. This is evident when you need to round calculated results to the significant digit that is furthest to the left and still within the precision of the original data. For instance, the result of 78,500 m - 362 m calculated to 78,138 m should be rounded to 78,100 m because the last significant figure of the original measurement was in the hundreds place (the '5'). When inputting data into a calculator or computer for determining a linear equation, rounding should be done to the appropriate number of significant figures. For example, rounding to four decimal places may be necessary depending on the context of the problem and required precision. If using trailing zeros in a number without a decimal point, utilize scientific notation to clearly indicate the number of significant figures. Scientific notation helps prevent confusion over which zeros are significant.