Okay so I'm doing doing significant figures in chem. And I was just wondering for problems like this:

Yes, you must convert because one cannot add dm to m.

I don't think the example you gave for exponents is what you meant. In the example you provided, it is a simple division and the answer may have 5 s.f. with the units of the answer being meters squared.

ca(clo3)2>cacl2+3o2

To work with significant figures, you need to follow certain rules. Let's break it down for the example you provided:

1. For the addition of .000456 dm and .00524 m:
- Since the units are different, you should convert them to the same unit before performing the addition.
- To convert dm to m, remember that 1 m = 10 dm. So, .000456 dm is equal to .0000456 m.
- Now, you have two values with the same unit: .0000456 m + .00524 m.
- Perform the addition: .0000456 m + .00524 m = .0052856 m.
- As for significant figures, the rule is to keep the same number of decimal places as the measurement with the fewest decimal places.
- In this case, .00524 m has 4 decimal places, so your answer will have 4 decimal places: .0052856 m.

2. For the division of 3845.2 m³ by 25.2354 m:
- For division, you need to consider the significant figures of both the numerator (3845.2 m³) and denominator (25.2354 m).
- Count the significant figures in each value. The number of significant figures depends on the rules of significant figures, such as leading zeros, trailing zeros, and zeros between significant figures.
- 3845.2 m³ has 5 significant figures.
- 25.2354 m has 6 significant figures.
- For division, the rule is to use the fewest significant figures from the values being divided.
- So, your division will have 5 significant figures: 3845.2 m³ / 25.2354 m = 152.31696 m³/m.

Remember to round your final answer according to the rules of significant figures.