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

Question

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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 \( (10^{-2})(-2) \).