How many significant figures are present in `0.010100xx10^3` ?

Options

A. 7
B. 5
C. 3
D. 10

Explanation

To determine how many significant figures are present in the number `0.010100 x 10^3`, we will follow a step-by-step approach based on the rules of significant figures.

### Step 1: Identify the number in standard form
The given number is `0.010100 x 10^3`. First, we can rewrite it in standard decimal form:
\[ 0.010100 x 10^3 = 10.100 \]

### Step 2: Analyze the leading zeros
In the number `10.100`, the leading zeros (the zeros before the first non-zero digit) are not significant. In this case, the leading zeros are part of the original number `0.010100` and are not counted as significant figures.

### Step 3: Identify significant figures
According to the rules of significant figures:
- All non-zero digits are significant.
- Any zeros between significant digits are also significant.
- Trailing zeros in the decimal portion are significant.

In `10.100`:
- The digits `1` and `0` (the first `0` after `1`) are significant.
- The `1` is significant.
- The `0` between `1` and `1` is significant.
- The two trailing zeros after the decimal point are also significant.

### Step 4: Count the significant figures
Now, let's count the significant figures in `10.100`:
- `1` (significant)
- `0` (significant)
- `1` (significant)
- `0` (significant)
- `0` (significant)

Thus, there are a total of **5 significant figures** in the number `0.010100 x 10^3`.

### Final Answer
The number of significant figures in `0.010100 x 10^3` is **5**.

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