The prefix milli means 1/1000. In exponential form, it is written as 10^-3. How do you suppose you would write kilo in exponential form? Why? I’m confused about this issue, can you help me?
The correct answer and explanation is:
Sure! The correct exponential form of kilo is:
10³ (which means 1,000)
Explanation (Approx. 300 words):
In the metric system, prefixes like milli, centi, and kilo are used to express large or small quantities more easily. Each prefix represents a specific power of 10. For example:
- Milli means 1/1000 or 0.001. This is the same as writing 10⁻³, since 10−3=1103=1100010^{-3} = \frac{1}{10^3} = \frac{1}{1000}.
- Kilo means 1,000 times the base unit. That means: 1 kilometer=1,000 metersor1 kilogram=1,000 grams1 \text{ kilometer} = 1,000 \text{ meters} \quad \text{or} \quad 1 \text{ kilogram} = 1,000 \text{ grams}
In exponential form, 1,000 is written as: 10310^3
This is because 103=10×10×10=1,00010^3 = 10 \times 10 \times 10 = 1,000.
So, just as milli- represents a division (a negative exponent), kilo- represents a multiplication (a positive exponent). Think of the exponent as a shortcut for how many times you’re multiplying or dividing by 10.
Understanding this helps in science and math because it simplifies very large or very small numbers. Instead of writing 0.000001 meters, for example, you could write 1 micrometer (µm), which is 10−610^{-6} meters. Similarly, instead of writing 1,000 meters, you just write 1 kilometer (km), which is 10310^3 meters.
To summarize:
- Milli- = 10−310^{-3} (1/1000)
- Kilo- = 10310^{3} (1,000)
The reason for the positive 3 in kilo (10³) is because it multiplies the base unit by 1,000 — the opposite of what milli- does.