Which symbol would you use to correctly compare? Draw a numberline to help you.

Question

6.2×10^−3 and 0 and 1(1 point)
Responses

6.2×10^−3<0 and 6.2×10−3<16.2×10−3<0 and 6.2×10^−3<1

6.2×10^−3<0 and 6.2×10−3>16.2×10−3<0 and 6.2×10^−3>1

0<6.2×10−3<10<6.2×10^−3<1

6.2×10^−3>0 and 6.2×10−3>16.2×10−3>0 and 6.2×10^−3>1
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Answer 1

To compare the number \( 6.2 \times 10^{-3} \), let's first evaluate it.

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

Now, we need to compare \( 0.0062 \) with \( 0 \) and \( 1 \).

• \( 0 \) is less than \( 0.0062 \) because \( 0.0062 \) is a positive number.
• \( 0.0062 \) is also less than \( 1 \) because it is much smaller than \( 1 \).

Thus, we can summarize this with the comparison:

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

Now, let's represent this on a number line:

|---|---|---|---|---|---|---|---|---|---|---|---|
-0.1                                          1
        |         0.0062
        |
        0

From the number line:

• \( 0 \) is at the left,
• \( 0.0062 \) (or \( 6.2 \times 10^{-3} \)) is a little to the right of \( 0 \),
• and \( 1 \) is further to the right.

Therefore, the correct response is:

0 < 6.2×10^−3 < 1.