Which expression leaves you with the largest number on the number line?(1 point)

Question

Responses

105⋅10−4⋅1011
10 to the 5th power times 10 to the negative 4 power times 10 to the 11th power

1018108
the fraction with numerator 10 to the 18th power and denominator 10 to the 8th power

1081014
the fraction with numerator 10 to the 8th power and denominator 10 to the 14th power

(10(−2))(−7)

Answer 1

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

1. \( 105 \cdot 10^{-4} \cdot 10^{11} \):

   • First, combine the powers of 10: \[ 10^{-4} \cdot 10^{11} = 10^{-4 + 11} = 10^{7}. \]
   • Now, multiply by 105: \[ 105 \cdot 10^{7} = 1.05 \cdot 10^{9} = 1.05 \times 10^{9}. \]

2. \( \frac{10^{18}}{10^{8}} \):

   • When dividing powers of 10, subtract the exponents: \[ 10^{18 - 8} = 10^{10}. \]

3. \( \frac{10^{8}}{10^{14}} \):

   • Again, subtract the exponents: \[ 10^{8 - 14} = 10^{-6}. \]
   • This results in a very small number, specifically \(0.000001\).

4. \( (10^{-2})(-7) \):

   • First, evaluate \(10^{-2}\): \[ 10^{-2} = 0.01. \]
   • Now, multiply: \[ 0.01 \cdot (-7) = -0.07. \]
   • This results in a negative value.

Now, let's summarize the results:

• \( 105 \cdot 10^{-4} \cdot 10^{11} \) = \( 1.05 \times 10^{9} \)
• \( \frac{10^{18}}{10^{8}} \) = \( 10^{10} \) = \( 10,000,000,000 \)
• \( \frac{10^{8}}{10^{14}} \) = \( 10^{-6} \) = \( 0.000001 \)
• \( (10^{-2})(-7) \) = \( -0.07 \)

Comparing all the numbers obtained, the largest number is:

\( 10^{10} \) or \( \frac{10^{18}}{10^{8}} \).