Question

Which symbol would you use to correctly compare? Draw a numberline to help you.6.2 × 10^−3 and 0 and 1


A. 6.2 × 10^−3 < 0 and 6.2 × 10^−3 >1
B. 0 < 6.2 × 10^−3 < 1
C. 6.2 × 10^−3 < 0 and 6.2 × 10^−3 < 1
D. 6.2 × 10^−3 > 0 and 6.2 × 10^−3 > 1

Answer 1

To compare \(6.2 \times 10^{-3}\) with 0 and 1, we first need to evaluate the value of \(6.2 \times 10^{-3}\).

Calculating it:

\[
6.2 \times 10^{-3} = 6.2 \times 0.001 = 0.0062
\]

With this value, we can compare it to 0 and 1:

- \(0.0062\) is greater than \(0\) because \(0.0062 > 0\).
- \(0.0062\) is less than \(1\) because \(0.0062 < 1\).

Thus, we can express this as:

\[
0 < 6.2 \times 10^{-3} < 1
\]

Now, let's look at the options provided:

A. \(6.2 \times 10^{-3} < 0\) and \(6.2 \times 10^{-3} > 1\) - This is incorrect.

B. \(0 < 6.2 \times 10^{-3} < 1\) - This is correct.

C. \(6.2 \times 10^{-3} < 0\) and \(6.2 \times 10^{-3} < 1\) - The first part is incorrect.

D. \(6.2 \times 10^{-3} > 0\) and \(6.2 \times 10^{-3} > 1\) - The second part is incorrect.

The correct answer is **B**: \(0 < 6.2 \times 10^{-3} < 1\).

### Number Line Representation

Here’s a simple illustration of how \(0.0062\) (which is \(6.2 \times 10^{-3}\)) fits on the number line relative to \(0\) and \(1\):

```
|---|---|---|---|---|---|---|---|---|---|---|---|
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
| |
|----------------|-------|
0 0.0062
```

Here, you can see \(0.0062\) is clearly greater than \(0\) and less than \(1\).