Question

Which expression leaves you with the smallest number on the number line?

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(1 point)
Responses

(10(−2))(−2)
open paren 10 to the negative 2 power close paren to the negative 2 power

10(8)/10(8)
the fraction with numerator 10 to the 8th power and denominator 10 to the 8th power

10(5)⋅10(−4)
10 to the 5th power times 10 to the negative 4 power

10(8)/10(10)

Answer 1

To find the expression that leaves you with the smallest number on the number line, let's evaluate each expression one by one:

1. **\( (10^{-2})(-2) \)**:
\( 10^{-2} = 0.01 \)
Thus, \( (0.01)(-2) = -0.02 \).

2. **\( \frac{10^8}{10^8} \)**:
This simplifies to \( 1 \).

3. **\( 10^5 \cdot 10^{-4} \)**:
Using the property of exponents, we combine them:
\( 10^{5 + (-4)} = 10^1 = 10 \).

4. **\( \frac{10^8}{10^{10}} \)**:
This simplifies to \( 10^{8 - 10} = 10^{-2} = 0.01 \).

Now, let's compile the findings:

- \( (10^{-2})(-2) = -0.02 \)
- \( \frac{10^8}{10^8} = 1 \)
- \( 10^5 \cdot 10^{-4} = 10 \)
- \( \frac{10^8}{10^{10}} = 0.01 \)

Among these values, the smallest number is **\(-0.02\)** from the expression \( (10^{-2})(-2) \).

Thus, the expression that leaves you with the smallest number on the number line is **\( (10^{-2})(-2) \)**.