To determine how many times less 102 is than 106, we can express this as a ratio:
\[ \frac{102}{106} \]
Calculating this gives:
\[ \frac{102}{106} = \frac{51}{53} \approx 0.9623 \]
To express how many times less 102 is compared to 106, we take the reciprocal:
\[ \frac{106}{102} \approx 1.0392 \]
This value is not yet in the form of an integer power of 10, so we can express how much smaller 102 is than 106 in terms of a base 10 representation.
Since \( 1.0392 \) can be approximated as \( 10^{0} \) (since it's close to 1), we won't directly see a power of ten here. However, let's calculate how many times 102 is less than 106:
The difference between 106 and 102 is:
\[ 106 - 102 = 4 \]
So, 102 is \( 4 \) units less than 106.
To express \( 4 \) in powers of \( 10 \), we can say:
\[ 4 \approx 10^{0.6021} \]
However, if the question strictly asks how many times less in terms of integer powers of 10 and the context is somewhat wanting to represent something conceptually related to the difference or ratio in a standardized integer power of ten representation, we might just evaluate it simply based on its two values:
Since you have options (including \( 0.0001 \)) it could mean we may be looking for something conceptual with \( 10^{-4} \) if viewed from a perspective in simplified numeric form difference.
But the calculated ratio is simply around \( 10^{0} \).
If the aim is purely how it is represented succinctly, \( 10^{-4} \) does not apply here directly.
The closest answer that fits how many times smaller 102 is compared to 106 broadly is an interpretation challenge leading to perhaps a conceptual miscommunication.
So if we just want to classify overall the best answer to fit among the choices given focusing on differences rather than simple average or ratios, the correct answer is 0.0001 or \(10^{-4}\) but it pertains to a relative misunderstand rather than calculated directly in this context.
So, the formal answer would be:
1 answer