Significant Figures Problems With Step-by-Step Answers (Solved Examples)

Understanding significant figures becomes much easier when you practice real problems with clear step-by-step answers. Many students know the rules but still get confused when applying them in calculations.

In this guide, you’ll find common significant figures problems, each solved step by step, so you can learn how and why each answer is correct.

Problem 1: How Many Significant Figures Are in 0.00450?

Step 1: Identify leading zeros

Leading zeros (0.00) are not significant.

Step 2: Count non-zero digits

The digits 4 and 5 are significant.

Step 3: Check trailing zeros

The zero at the end is after a decimal point, so it is significant.

✅ Final Answer

0.00450 has 3 significant figures

Problem 2: How Many Significant Figures Are in 1500?

Step 1: Count non-zero digits

Digits 1 and 5 are significant.

Step 2: Look at trailing zeros

There is no decimal point, so trailing zeros are not significant.

✅ Final Answer

1500 has 2 significant figures

Problem 3: Round 23.746 to 3 Significant Figures

Step 1: Identify the first three significant digits

2, 3, and 7

Step 2: Look at the next digit

The next digit is 4, which is less than 5.

Step 3: Decide whether to round up

Since 4 < 5, do not round up.

✅ Final Answer

23.746 rounded to 3 significant figures is 23.7

Problem 4: Round 0.09995 to 3 Significant Figures

Step 1: Ignore leading zeros

Leading zeros are not significant.

Step 2: Identify first three significant digits

9, 9, and 9

Step 3: Look at the next digit

The next digit is 5, so we round up.

Step 4: Handle rounding carefully

0.09995 becomes 0.100

✅ Final Answer

0.100 (3 significant figures)

Problem 5: How Many Significant Figures Are in 6.020 × 10³?

Step 1: Look only at the coefficient

Ignore ×10³.

Step 2: Count digits in 6.020

Digits 6, 0, 2, and the trailing zero after the decimal are all significant.

✅ Final Answer

6.020 × 10³ has 4 significant figures

Problem 6: Multiply and Apply Significant Figures

2.4 × 3.56

Step 1: Multiply the numbers

2.4 × 3.56 = 8.544

Step 2: Count sig figs in original numbers

  • 2.4 → 2 sig figs
  • 3.56 → 3 sig figs

Step 3: Use the smallest number of sig figs

Final answer must have 2 significant figures.

Step 4: Round the result

8.544 → 8.5

✅ Final Answer

8.5 (2 significant figures)

Problem 7: Addition With Significant Figures

12.11 + 0.3

Step 1: Identify decimal places

  • 12.11 → 2 decimal places
  • 0.3 → 1 decimal place

Step 2: Add the numbers

12.11 + 0.3 = 12.41

Step 3: Round to the least decimal places

Round to 1 decimal place.

✅ Final Answer

12.4

Common Mistakes Students Make

  • Counting leading zeros as significant
  • Forgetting to round after calculations
  • Using sig-fig rules incorrectly in addition/subtraction
  • Ignoring scientific notation rules

Practicing step by step helps avoid these errors.

Why Practice Significant Figures Problems?

Step-by-step practice helps you:

  • Understand the rules clearly
  • Avoid exam mistakes
  • Improve lab report accuracy
  • Gain confidence in science calculations

Use an Online Significant Figures Calculator

After solving problems manually, it’s smart to verify your answers using a reliable online significant figures calculator. It helps confirm:

  • Correct sig fig count
  • Proper rounding
  • Error-free results

Final Thoughts

Significant figures are not about memorizing rules — they’re about applying them correctly. When you solve problems step by step, everything becomes logical and manageable.

Practice regularly, check your answers, and significant figures will no longer feel confusing.

FAQs

How to solve problems with significant figures?

To solve problems with significant figures, first identify how many significant figures each number has. Perform the calculation, then round the final answer to the same number of significant figures as the value with the fewest sig figs. For addition and subtraction, round based on decimal places instead of significant figures.

How many significant figures are there in 0.310 × 10³?

The number 0.310 × 10³ has 3 significant figures.

Only the digits in the coefficient (0.310) are counted. The digits 3, 1, and the trailing zero after the decimal point are all significant.

How do you write 57.3997 correctly to 4 significant figures?

The number 57.3997 rounded to 4 significant figures is 57.40.

The first four significant digits are 5, 7, 3, and 9. The next digit (9) causes the last digit to round up, and the trailing zero is kept to show precision.

How to determine the correct number of sig figs?

To determine the correct number of significant figures, count all non-zero digits, include zeros between non-zero digits, and count trailing zeros only if a decimal point is present. Ignore leading zeros. In scientific notation, count only the digits in the coefficient.

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