Significant Figures Rules | Question-Answer, FAQS, Worksheet, MCQS, Test Paper

What are Significant Figures?

Significant figures are the digits in a number that carry meaningful information about its precision. When performing scientific calculations, it is essential to know how many significant figures should be considered to ensure accuracy.

Rules for Counting Significant Figures

For counting significant figures, we make use of the rules listed hereunder:

(a) All Non-Zero Digits are Significant

Any number that is not zero counts as a significant figure.

• Example: x = 2567 has four significant figures.

Examples :

• 42.3 has three significant figures.
• 243.4 has four significant figures.
• 24.123 has five significant figures

(b) Zeroes Between Non-Zero Digits are Significant

The zeroes appearing between two non-zero digits are counted in significant figure

• Example: 6.028 has four significant figures.

Examples :

• 5.03 has three significant figures.
• 5.604 has four significant figures.
• 4.004 has four significant figures

(c) Leading Zeroes are Not Significant

The zeroes located to the left of the last non-zero digit are not significant.

• Example: 0.0042 has two significant figures.

Examples :

• 0.543 has three significant figures.
• 0.045 has two significant figures.
• 0.006 has one significant figures

(d) Trailing Zeroes in Numbers Without a Decimal are Not Significant

In a number without decimal, zeroes located to the right of the non-zero digit are not significant. However, when some value is assigned on the basis of actual measurement, then the zeroes to the right non-zero digit become significant.

• For example, L = 20 m has two significant figures but x = 200 has only one significant figure.
• Example: x=200 has only one significant figure, however, if written as 20.0, it has three significant figures.

(e) Trailing Zeroes in Numbers with a Decimal are Significant

If a number has a decimal, all zeroes to the right of the last non-zero digit are significant.

• Example: x=1.400 has four significant figures.

Examples :

• 4.330 has four significant figures.
• 433.00 has five significant figures.
• 343.000 has six significant figures.

(f) Powers of Ten are Not Counted as Significant Figures

The exponent in scientific notation does not contribute to the significant figures.

• Example: 1.4 x 10⁻⁷ has two significant figures i.e., 1 and 4.

Examples :

• 1.32 × 10^–2 has three significant figures.
• 1.32 × 10⁴ has three significant figures.

(g) Change in Units Does Not Affect Significant Figures

Change in the units of measurement of a quantity, however, does not change the number of significant figures. For example, suppose the distance between two stations is 4067 m. It has four significant figures. The same distance can be expressed as 4.067 km or 4.067 ×10⁵ cm. In all these expressions, however, the number of significant figures continues to be four.

Table of Significant Figures

Exam-Oriented Questions

Multiple-Choice Questions (MCQs)

1. How many significant figures does the number 0.00560 have?
   • (a) 2
   • (b) 3 ✅
   • (c) 4
   • (d) 5
   • Explanation: The leading zeroes are not counted, and 560 has three significant figures.
2. Which of the following numbers has four significant figures?
   • (a) 20.00 ✅
   • (b) 2000
   • (c) 0.020
   • (d) 1.002 ✅
   • Explanation: 20.00 has four significant figures because trailing zeroes in a decimal are counted. 1.002 also has four significant figures.

Conceptual Questions

Q1: Why are significant figures important in scientific calculations?

• Answer: Significant figures indicate the precision of a measurement and help in reducing errors in calculations.

Q2: Why does 1000 have only one significant figure while 1000.0 has five?

• Answer: In 1000, the trailing zeroes are not considered significant unless there is a decimal. 1000.0 explicitly indicates a precise measurement with five significant figures.

Do You Know?

• A number like 0.000560 has three significant figures because the leading zeroes are not counted.
• Writing a number in scientific notation makes it easier to identify significant figures. Example: 3.40 x 10³ has three significant figures.
• When performing calculations, the result should be rounded to match the least number of significant figures in the given data.

Worksheet

1. Determine the number of significant figures in each of the following:
   • (a) 0.00250
   • (b) 45.00
   • (c) 6.0008
   • (d) 7.1 × 10³
   • (e) 300
2. State whether the following statements are True or False:
   • (a) Zeroes after a decimal point are always significant.
   • (b) 100.0 has three significant figures.
   • (c) 4.007 has four significant figures.
   • (d) 0.0001 has one significant figure.

Test Paper (10 Marks)

Section A: MCQs (2 Marks)

1. How many significant figures are in the number 0.003020? (1 Mark)
2. Identify the number of significant figures in 2500.0. (1 Mark)

Section B: Short Answer Questions (4 Marks)

3. Explain why 500 has only one significant figure but 500.0 has four. (2 Marks)
4. Convert 0.000340 into scientific notation and identify the number of significant figures. (2 Marks)

Section C: Long Answer Questions (4 Marks)

5. Why do significant figures matter in real-world calculations such as engineering and medicine? Support your answer with examples. (4 Marks)

Quick Revision Points

✅ Non-zero digits are always significant.

✅ Zeroes between non-zero digits are significant.

✅ Leading zeroes are NOT significant.

✅ Trailing zeroes in decimal numbers ARE significant.

✅ Powers of ten in scientific notation are NOT counted as significant figures.

✅ Unit conversions do NOT change significant figures.

Test Your Knowledge (Quiz)

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