Question

Which of the following rules regarding the significant figures and calculations involving them is not correct? (a) The result of an addition or subtraction is reported to the same number of decimal places as present in number with least decimal places. (b) Result of multiplication or division should have same number of significant figures as present in most precise figure. (c) The result of multiplication or division should be rounded off to same number of significant figures as present in least precise figure. (d) Thenon-significantfiguresinthemeasurements are rounded off.

Short answer

The incorrect rule regarding significant figures is (b) because the result of multiplication or division should have the same number of significant figures as present in the least precise figure, not the most precise figure.

Step-by-step solution

Understanding the concept of significant figures

Significant figures are the digits in a number that carry meaningful contributions to its precision. This includes all digits except: leading zeros, trailing zeros (only when they are used to indicate the precision of the number), and any spurious digits. The rules for operations with significant figures must be known in order to identify the incorrect rule.

Analyzing each rule

Evaluate each given rule one by one in the context of standard rules for significant figures in arithmetic operations. (a) The least number of decimal places in addition or subtraction determines the number of decimal places in the result. (b) The number of significant figures in the most precise figure should determine those in the result of multiplication or division (incorrect according to standard rules). (c) The least number of significant figures in any number of the problem determines the number of significant figures in the answer for multiplication or division. (d) Non-significant figures are not typically rounded off; they are removed during the rounding process.

Identifying the incorrect rule

Upon evaluation, (b) states that the result should have the same number of significant figures as the 'most' precise figure, which is not the correct rule. The correct rule is that the result should have the same number of significant figures as the 'least' precise figure for multiplication or division.

Key concepts

Significant Figures Rules

In chemistry, understanding significant figures is crucial for conveying the precision of measurements and calculations. Significant figures, or 'sig figs', are the digits in a measurement that are known with certainty plus one final digit, which is somewhat uncertain or estimated.

Here are some basic rules governing significant figures:

• Non-zero digits are always significant.
• Any zeros between non-zero digits are significant.
• Leading zeros (zeros before non-zero digits) are not significant. They're only placeholders.
• Trailing zeros in a number containing a decimal point are significant.
• Trailing zeros in a number without a decimal point may or may not be significant, depending on whether they're placeholders or indicate measurement precision.
• Exact numbers (like 100 in 1 meter = 100 cm) have an infinite number of significant figures because they are counting numbers or definitions.

Applying these rules will ensure that you retain the precision of your measurements without overestimating the certainty of your results.

Arithmetic Operations in Chemistry

Performing arithmetic operations while considering significant figures is essential to maintain the integrity of the data's precision. In chemistry, when carrying out these calculations, specific guidelines should be followed.

Addition and Subtraction

For addition and subtraction, the result should have the same number of decimal places as the term with the least number of decimal places.

Multiplication and Division

With multiplication and division, on the other hand, it's the count of significant figures that takes the spotlight. The final result should match the term with the least number of significant figures. This is where the common mistake from the exercise lies; it's not about matching the most precise term, but rather the least precise in terms of significant figures.
This sensitivity to the precision of our calculations helps us remain honest about the potential uncertainty inherent in every measurement and calculation in chemistry.

Precision in Chemical Measurements

Precision in chemical measurements is indicative of how closely multiple measurements or calculations agree with each other. It highlights the consistency of results, and significant figures play a key role in indicating this precision.

To ensure accuracy and precision, chemists use calibrated instruments and standardize their procedures, but even the most careful measurements have some degree of uncertainty, which is where significant figures become informative. Recording figures beyond the significant ones may incorrectly suggest a higher level of precision than the measurement justifies.

By diligently applying significant figure rules in reporting and calculations, chemists communicate the reliability of their data. This practice allows others to understand the possible variability in the findings, fostering trust and repeatability in scientific inquiry. Keeping significant figures in mind helps uphold the standards of careful measurement and reliable data interpretation in the field of chemistry.