Question
Which expression leaves you with the smallest number on the number line?
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(1 point)
Responses
105⋅10−4
10 to the 5th power times 10 to the negative 4 power
1081010
the fraction with numerator 10 to the 8th power and denominator 10 to the 10th power
108108
the fraction with numerator 10 to the 8th power and denominator 10 to the 8th power
(10−2)−2
open paren 10 to the negative 2 power close paren to the negative 2 power
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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
1081010
the fraction with numerator 10 to the 8th power and denominator 10 to the 10th power
108108
the fraction with numerator 10 to the 8th power and denominator 10 to the 8th power
(10−2)−2
open paren 10 to the negative 2 power close paren to the negative 2 power
Skip to navigation
Answers
GPT-4o mini
To determine which expression results in the smallest number, let's evaluate each option:
1. **\(105 \cdot 10^{-4}\)**:
- This expression simplifies to \(105 \cdot 0.0001 = 0.0105\).
2. **\(\frac{10^8}{10^{10}}\)**:
- Using the properties of exponents, this simplifies to \(10^{8-10} = 10^{-2} = 0.01\).
3. **\(\frac{10^8}{10^8}\)**:
- This simplifies to \(10^{8-8} = 10^0 = 1\).
4. **\((10^{-2})^{-2}\)**:
- Using the rule \((a^m)^n = a^{m \cdot n}\), this simplifies to \(10^{-2 \cdot -2} = 10^{4} = 10000\).
Now let's summarize the results:
- \(105 \cdot 10^{-4} = 0.0105\)
- \(\frac{10^8}{10^{10}} = 0.01\)
- \(\frac{10^8}{10^8} = 1\)
- \((10^{-2})^{-2} = 10000\)
Comparing the values:
- \(0.0105\)
- \(0.01\)
- \(1\)
- \(10000\)
The smallest value is \(0.01\), which corresponds to the expression \(\frac{10^8}{10^{10}}\). Therefore, the expression that leaves you with the smallest number on the number line is:
**\(\frac{10^8}{10^{10}}\)**
1. **\(105 \cdot 10^{-4}\)**:
- This expression simplifies to \(105 \cdot 0.0001 = 0.0105\).
2. **\(\frac{10^8}{10^{10}}\)**:
- Using the properties of exponents, this simplifies to \(10^{8-10} = 10^{-2} = 0.01\).
3. **\(\frac{10^8}{10^8}\)**:
- This simplifies to \(10^{8-8} = 10^0 = 1\).
4. **\((10^{-2})^{-2}\)**:
- Using the rule \((a^m)^n = a^{m \cdot n}\), this simplifies to \(10^{-2 \cdot -2} = 10^{4} = 10000\).
Now let's summarize the results:
- \(105 \cdot 10^{-4} = 0.0105\)
- \(\frac{10^8}{10^{10}} = 0.01\)
- \(\frac{10^8}{10^8} = 1\)
- \((10^{-2})^{-2} = 10000\)
Comparing the values:
- \(0.0105\)
- \(0.01\)
- \(1\)
- \(10000\)
The smallest value is \(0.01\), which corresponds to the expression \(\frac{10^8}{10^{10}}\). Therefore, the expression that leaves you with the smallest number on the number line is:
**\(\frac{10^8}{10^{10}}\)**