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

Question

Number Line" Images – Browse 1,129 Stock Photos, Vectors ...



(1 point)
Responses

10⁵ ⋅10−⁴
10 to the 5th power times 10 to the negative 4 power

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

10⁸ / 10⁸
the fraction with numerator 10 to the 8th power and denominator 10 to the 8th power

10⁸/10¹⁰

Answer 1

To determine which expression yields the smallest number, let's evaluate each expression step by step.

1. \( 10^5 \cdot 10^{-4} \): \[ 10^5 \cdot 10^{-4} = 10^{5-4} = 10^1 = 10 \]

2. \( (10^{-2})^{-2} \): \[ (10^{-2})^{-2} = 10^{-2 \cdot -2} = 10^4 = 10,000 \]

3. \( \frac{10^8}{10^8} \): \[ \frac{10^8}{10^8} = 10^{8-8} = 10^0 = 1 \]

4. \( \frac{10^8}{10^{10}} \): \[ \frac{10^8}{10^{10}} = 10^{8-10} = 10^{-2} = 0.01 \]

Now we compare the results:

• \( 10^5 \cdot 10^{-4} = 10 \)
• \( (10^{-2})^{-2} = 10,000 \)
• \( \frac{10^8}{10^8} = 1 \)
• \( \frac{10^8}{10^{10}} = 0.01 \)

The smallest number on the number line among these results is: \[ \frac{10^8}{10^{10}} = 0.01 \]

So, the expression that leaves you with the smallest number on the number line is: \[ \frac{10^8}{10^{10}} \]