Animated Solution for Chemistry - Basic Concepts in Chemistry: The number of significant figures in $50000.020\times 10^{-3}$ is ............ .

Imagine you are a scientist in a high-tech laboratory, measuring the mass of a microscopic sample.

The number you record is not just a random string of digits; it is a story of precision.

When we look at the value $50000.020\times 10^{-3}$, we are looking at a highly precise measurement.

Our goal is to determine exactly how many digits in this number carry meaningful physical information. These are what we call significant figures.

The Order of Magnitude

The first thing that catches our eye is the exponential term, $10^{-3}$.

In scientific notation, this term simply tells us the scale or the order of magnitude of the measurement. It dictates where the decimal point should be placed if we were to write the number in standard form.

Because it only provides scale and not precision, the power of 10 is never counted as a significant figure.

We can safely ignore the $10^{-3}$ for our counting purposes.

The Anchors (Non-Zero Digits)

Now, let's focus on the main numerical part: $50000.020$.

The most fundamental rule of significant figures is that all non-zero digits are always significant.

In our number, we have the digits $5$ and $2$. These act as our anchors. They represent definite, measured quantities.

So, right off the bat, we have $2$ significant figures.

The Trapped Zeros

Next, we look at the zeros. Zeros can be tricky, but their position tells us everything.

Look at the zeros located between our anchors, $5$ and $2$.

The rule states that any zeros trapped between two significant digits are also significant.

Why? Because if the $5$ and the $2$ are precisely known, every digit between them must also be precisely known.

Counting them up, we have four zeros before the decimal point and one zero after the decimal point. That gives us $5$ trapped zeros.

Adding these to our anchors, we now have $7$ significant figures.

The Trailing Zeros

Finally, we reach the very end of the number. There is a single zero sitting after the $2$.

This is a trailing zero. The rule for trailing zeros is clear: if a number contains a decimal point, all trailing zeros are significant.

A scientist wouldn't write that final zero unless their instrument was precise enough to measure it. It is a deliberate statement of accuracy.

Therefore, this final zero is also significant.

Let's tally up our final count.

We have $1$ non-zero digit at the start, $5$ trapped zeros, $1$ non-zero digit near the end, and $1$ trailing zero.

The true number of significant figures is $8$.

However, if you look at the official answer key for this JEE question, it states the answer is $7$.

Why the discrepancy? The official solution fell into a classic trap! They correctly identified the non-zero digits and the trapped zeros, counting from the $5$ to the $2$, which gives exactly $7$ digits.

But they completely forgot to apply the rule for the trailing zero!

While the official key may say $7$, as a student of science, you must understand the rigorous rules. The mathematically and scientifically correct answer is $8$.