Let's go through the steps to determine how many times larger one unit of volume is compared to another using the given table of metric volume measures represented as powers of 10.
1. Understanding the Powers of 10:
Centiliter: [tex]\( 10^{-2} \)[/tex]
Liter: [tex]\( 10^0 \)[/tex]
Hectoliter: [tex]\( 10^2 \)[/tex]
Kiloliter: [tex]\( 10^3 \)[/tex]
* Megaliter: [tex]\( 10^6 \)[/tex]
2. Comparing Megaliter to Hectoliter:
To find how many times larger a megaliter is compared to a hectoliter, we divide the power of 10 for the megaliter by the power of 10 for the hectoliter.
[tex]\[
\frac{10^6}{10^2} = 10^{6-2} = 10^4 = 10,000
\][/tex]
This shows that a megaliter is 10,000 times larger than a hectoliter.
3. Comparing Kiloliter to Centiliter:
To find how many times larger a kiloliter is compared to a centiliter, we divide the power of 10 for the kiloliter by the power of 10 for the centiliter.
[tex]\[
\frac{10^3}{10^{-2}} = 10^{3-(-2)} = 10^{3+2} = 10^5 = 100,000
\][/tex]
This shows that a kiloliter is 100,000 times larger than a centiliter.
4. Comparing Hectoliter to Centiliter:
To find how many times larger a hectoliter is compared to a centiliter, we divide the power of 10 for the hectoliter by the power of 10 for the centiliter.
[tex]\[
\frac{10^2}{10^{-2}} = 10^{2-(-2)} = 10^{2+2} = 10^4 = 10,000
\][/tex]
This shows that a hectoliter is 10,000 times larger than a centiliter.
So, the solutions are:
- A megaliter is 10,000 times larger than a hectoliter.
- A kiloliter is 100,000 times larger than a centiliter.
- A hectoliter is 10,000 times larger than a centiliter.
