Q.The number of significant figures in 0.06900 is

Concept: Significant figures – counting rules for zeros

The rules are:

1. All non-zero digits are significant
2. Zeros between non-zero digits are significant
3. Leading zeros (before the first non-zero digit) are never significant
4. Trailing zeros after the decimal point are significant

For $0.06900$:

• The leading zeros ($0.0$) are placeholders, not significant
• The digits $6$, $9$ are non-zero, so significant
• The two trailing zeros ($00$) after $69$ come after the decimal point, so both are significant

Counting: $6$, $9$, $0$, $0$ → four significant figures.

Understanding Significant Figures

Significant figures tell us about the precision of a measurement. They represent all the digits we are confident about, plus one uncertain digit. The challenge with zeros is knowing when they're placeholders (showing scale) versus when they carry information about precision.

The rules crystallize around one principle: trailing zeros after the decimal point, following a non-zero digit, are always significant because you wouldn't write them unless your measuring instrument justified that precision.

Analyzing 0.06900

Let me walk through this number digit by digit:

1. The leading zero before the decimal (0.) is never significant. It's just notation—we could write this as .06900 in some contexts. This zero tells us nothing about measurement precision.

2. The zero immediately after the decimal (0.0...) is also not significant. It's a placeholder showing that our number is in the hundredths range or smaller. If we expressed this in scientific notation as $6.900 \times 10^{-2}$, this zero would disappear entirely.

3. The digit 6 is our first non-zero digit. This is significant—it's the first digit that carries actual measurement information.

4. The digit 9 is significant. Any non-zero digit is always significant.

5. The first trailing zero (0.0690_) is significant. Once we've started counting significant figures after a non-zero digit, all subsequent digits matter.

6. The final trailing zero (0.06900) is also significant. This is the key insight: you wrote this zero deliberately to show your measurement was precise to five decimal places. If your instrument only measured to $0.069$, you would have stopped there.

Counting our significant figures: 6, 9, 0, 0 gives us four significant figures total.

Concept: Significant Figures in a Decimal Number

The number of significant figures in a decimal number depends on the position of zeros — leading zeros are never significant, but trailing zeros after a decimal point are significant.

Method: Rule-Based Counting for Decimal Numbers

Steps:

1. Identify the decimal point — the number is $0.06900$, which is less than 1.

2. Ignore all leading zeros (zeros to the left of the first non-zero digit).

   • Here, the first non-zero digit is 6.
   • The zeros before it ($0.0$) are not significant.

3. Count all digits from the first non-zero digit onward, including trailing zeros after the decimal.

   • Digits after the first non-zero digit: $6, 9, 0, 0$
   • That’s 4 digits.

4. Trailing zeros after the decimal are significant because they indicate the precision of the measurement.

Final Answer:

The number of significant figures in $0.06900$ is $\boxed{4}$.

So the correct option is (B) 4.

Common Mistakes in Counting Significant Figures for 0.06900

Students often struggle with leading zeros and trailing zeros after a decimal. Here are the most frequent errors and how to avoid them.

✗ Mistake 1: Counting leading zeros as significant

What students do:

They see 0.06900 and count the zeros before the 6 — thinking the answer is 5 (option A).

Why it’s wrong:

Leading zeros only serve to locate the decimal point. They are never significant.

How to avoid:

Rule: Ignore all zeros to the left of the first non-zero digit.

In 0.06900, the first non-zero digit is 6. So leading zeros are not counted.

✗ Mistake 2: Ignoring trailing zeros after the decimal

What students do:

They see 0.06900 and think only 6 and 9 matter — giving 2 (option C).

Why it’s wrong:

Trailing zeros after a decimal are significant — they indicate the precision of the measurement.

How to avoid:

Rule: Every zero after the decimal and after a non-zero digit is significant.

Here, 0.06900 → digits: 6, 9, 0, 0 → 4 significant figures.

✗ Mistake 3: Confusing with numbers without a decimal

What students do:

They treat 0.06900 like 6900 (where trailing zeros may or may not be significant).

Why it’s wrong:

The decimal point changes the rule. Without a decimal, trailing zeros are ambiguous. With a decimal, they are always significant.

How to avoid:

Rule: If a decimal point is present, all zeros after the last non-zero digit are significant.

0.06900 has a decimal → the two zeros after 9 count.

✓ Correct Answer

0.06900 has 4 significant figures → Option (B).

Final count: 4 significant figures.

Quick Checklist to Avoid These Mistakes

1. Locate the first non-zero digit — start counting from there.
2. Count all digits after it — including zeros.
3. If decimal is present, trailing zeros are always significant.
4. If no decimal, trailing zeros are ambiguous — avoid that trap here.