Significant figures are defined as the digits in a number that are known reliably and indicate the precision of a measurement. This concept is crucial for understanding how much confidence one can have in the reported value.

In 0.00450, the leading zeros are not counted while the digits 4, 5, and the trailing 0 (which indicates measured precision) are significant. Therefore, the measurement has 3 significant figures.

Proper scientific notation requires a coefficient between 1 and 10. Option B (4.50 x 10^2) meets this criterion, while the others do not adhere to this standard format.

Leading zeros are used solely to position the decimal point and do not reflect measured precision. Therefore, they are never counted as significant figures.

For multiplication and division, the rule is to match the final result with the measurement that has the fewest significant figures. This ensures the result does not overstate the precision of the data.

The presence of a decimal point in 100.0 means that all zeros are considered significant. Thus, the number has 4 significant figures since each digit contributes to its precision.

For addition and subtraction, the result should be rounded to the smallest number of decimal places found among the measurements. This maintains the integrity of the precision in the calculation.

Without a decimal point, the trailing zeros in a whole number are typically not considered significant unless otherwise indicated. Hence, 2300 is taken to have only 2 significant figures.

Both adding a decimal point (e.g., 2300.) and expressing the number in scientific notation are accepted methods to denote that trailing zeros are meaningful. These approaches clarify the level of precision intended.

In 0.00789, the leading zeros are not significant and are only placeholders. The digits 7, 8, and 9 are the only significant figures, yielding a total of 3.

In multiplication, the final answer must be rounded to the same number of significant figures as the least precise measurement. Since 3.2 has 2 significant figures, the product should also be expressed with 2 significant figures.

The precision of a calculated result like density is limited by the least precise measurement used in the calculation. This rule ensures that the reported density does not imply more accuracy than the measurements allow.

To round 6.789 to two significant figures, you focus on the first two digits and look at the third digit to decide rounding. Since the third digit is 9, the number rounds up to 6.8.

In addition and subtraction, the final answer should be rounded to the least number of decimal places present in any of the measurements. Since 15.5 is precise to one decimal place, the result must be rounded accordingly.

To convert 0.00052 to scientific notation while retaining two significant figures, move the decimal so that only the non-zero digits remain in the coefficient. The correct representation is 5.2 x 10^-4.

Dividing 2.50 x 10^3 by 1.2 x 10^1 gives a preliminary result of approximately 208.33, but you must round to the least number of significant figures present - in this case, 2 significant figures. Representing the answer as 2.1 x 10^2 meets this requirement.

First, convert 0.0450 m to centimeters to get 4.50 cm. Adding 12.3 cm and 4.50 cm yields 16.8 cm, and because the least precise measurement (12.3 cm) has one decimal place, the result is given to one decimal place.

In 0.00670 g, the leading zeros are not counted, while the digits 6, 7, and the trailing zero (which is significant because of the decimal point) are all counted. This gives a total of 3 significant figures.

Significant figures are a critical way to communicate the precision of a measurement, indicating the reliability of the data. They prevent one from implying a greater degree of accuracy than the measurements support.

The leading zeros in 0.000120000 are not counted, but from the first non-zero digit onward (1, 2 followed by four zeros), every digit is significant since the decimal point confirms their precision. Thus, the number contains 6 significant figures.