CBSE Class 11th What are the significant figures Details & Preparations Downloads

What are the significant figures ?

Significant figures, also known as significant digits or sig figs, are a way of expressing the precision of measured or calculated values in science and mathematics. The number of significant figures in a value indicates the degree of certainty or precision associated with that value.

Here are the basic rules for determining significant figures:

1. Non-zero digits are always significant.

2. Any zeros between significant digits are also significant.

3. Leading zeros (zeros to the left of the first nonzero digit) are not significant.

4. Trailing zeros in a decimal number are significant.

5. Trailing zeros in a whole number without a decimal point may or may not be significant.

6. Exact numbers have an infinite number of significant figures.

Non-zero digits are always significant :-  Non-zero digits are always significant means that any digit that is not zero is considered significant. In a measured or calculated quantity, significant figures are the digits that carry meaningful information.

Example :- in the number 3456, each digit (3, 4, 5, and 6) is significant.

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Any zeros between significant digits are also significant :- Any zeros between significant digits are also significant" refers to the rules for determining the number of significant figures in a measured quantity. Significant figures are the digits in a measurement that contribute to its precision.

Example :- In the number 5004, all the digits (5, 0, 0, and 4) are significant.

Leading zeros (zeros to the left of the first nonzero digit) are not significant :- In the context of numerical values, leading zeros refer to zeros that appear to the left of the first nonzero digit in a number. When dealing with measurements or quantities, leading zeros are typically considered insignificant, meaning they do not affect the value of the number.

Example: The number "0056" is considered equivalent to "56."

Trailing zeros in a decimal number are significant :- In the context of decimal numbers, trailing zeros refer to the zeros that appear to the right of the last nonzero digit in a number. Whether or not trailing zeros are considered significant depends on the specific rules of measurement and the context in which the number is used.

Example :- In the number 120.30, all the digits (1, 2, 0, 3, and 0) are significant.

Trailing zeros in a whole number without a decimal point may or may not be significant :- In a whole number without a decimal point, trailing zeros may or may not be significant, depending on the context.If the number is written without a decimal point, trailing zeros are generally not considered significant. For example, the number "120" is usually considered to have two significant figures. The trailing zero is there to indicate the magnitude of the number but does not contribute to its precision.

Example :- in the number 1200, the zeros may or may not be considered significant. It's often clearer to use scientific notation (e.g., 1.20 × 10^3) to avoid ambiguity.

Exact numbers (defined values) have an infinite number of significant figures :- Exact numbers, also known as defined values or counted numbers, do not have a specified number of significant figures. Unlike measured numbers, which depend on the precision of the measuring instrument and have a finite number of significant figures, exact numbers are known with certainty and are not the result of measurement.

Example :- if a length is defined as exactly 5 metres, the number 5 has an infinite number of significant figures.

Why Are Significant Figures Important?

The use of significant figures is important in scientific work to communicate the precision of measurements and calculations. When performing mathematical operations with measured values, the result should be reported with the appropriate number of significant figures to maintain accuracy and reflect the precision of the original data. The rules for significant figures help scientists and researchers convey the reliability of their results.

SAMPLE PRACTICE QUESTIONS OF SIGNIFICANT FIGURES :

Q1. What Are Significant Figures?

Answer: Significant figures, also known as sig figs or significant digits, are the digits in a numerical value that contribute to its precision. They include all certain digits and the first uncertain digit.

Q2. Why Are Significant Figures Important in Measurements?

Answer: Significant figures convey the precision of a measurement. They help maintain accuracy and indicate the reliability of the data obtained through measurements.

Q3. How Do You Determine the Number of Significant Figures in a Number?

Answer: Count all non-zero digits, any zeros between non-zero digits, and any trailing zeros in a decimal number. Leading zeros in a whole number are not considered significant.

Q4. Are Leading Zeros Considered Significant Figures?

Answer: No, leading zeros (zeros to the left of the first non-zero digit in a whole number) are not considered significant figures. They are considered placeholders.

Q5. Are Trailing Zeros Significant Figures?

Answer: Trailing zeros in a decimal number are considered significant figures. In a whole number without a decimal point, trailing zeros may or may not be significant depending on the context.

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