The number of significant figures in 0.00340 is _________

We have to find the number of significant figures present in the decimal number $$0.00340$$. To do this, let us first recall the rules that govern significant figures in any measured quantity.

Rule 1: All non-zero digits $$\,(1,2,3,4,5,6,7,8,9)\,$$ are always significant.

Rule 2: Any zeros lying between two non-zero digits are significant. This is sometimes called the “captive zero” rule.

Rule 3: Leading zeros, that is, zeros written only to set the position of the decimal point, are not significant.

Rule 4: Trailing zeros in a number containing a decimal point are significant because they show the measured precision.

Now we apply these rules one by one to the given number $$0.00340$$.

First, let us write out the individual digits, underlining them one by one to decide whether each is significant or not:

$$0.\;0\;0\;3\;4\;0$$

In words, the figure reads: “zero point zero zero three four zero.” We label the positions so that we can reason clearly:

$$0.(\text{decimal})\underbrace{00}_{\text{leading zeros}}3\,4\,0$$

Step by step, we apply each rule:

1. The first two zeros after the decimal point are leading zeros. According to Rule 3, such zeros merely fix the position of the decimal point; hence they are not counted as significant.

2. Next comes the digit $$3$$. Since $$3$$ is a non-zero digit, Rule 1 tells us it is always significant. Thus we have our first significant figure.

3. Immediately after $$3$$ we have the digit $$4$$. Again, $$4$$ is non-zero, so by Rule 1 it is significant. Now we have two significant figures counted so far.

4. Finally, we find a zero written after the digit $$4$$, and importantly, the number has a decimal point. This zero is a trailing zero in a decimal. Rule 4 tells us that such zeros are significant because they indicate the precision up to that decimal place. Hence this zero is also counted.

No more digits remain. Summarising, the digits that are significant are:

$$\color{blue}{3},\quad\color{blue}{4},\quad\color{blue}{0}$$

That gives a total count of

$$\text{Number of significant figures}=3$$

So, the answer is $$3$$.