Sure, let's break this problem down step-by-step.
Step 1: Writing down the given areas in scientific notation.
- The area of the South China Sea is given as [tex]\( 8 \,003 \times 10^5 \)[/tex] km².
- The area of the Arctic Ocean is given as [tex]\( 1 \,405.6 \times 10^4 \)[/tex] km².
Step 2: Converting the areas to the same power of 10 for addition.
- For the South China Sea, we already have the area in scientific notation with [tex]\( 10^5 \)[/tex] km².
- For the Arctic Ocean, however, the area is in [tex]\( 10^4 \)[/tex] km². To be consistent, we need to convert it to [tex]\( 10^5 \)[/tex] km².
To convert [tex]\( 1 \,405.6 \times 10^4 \)[/tex] km² to a consistent power of [tex]\( 10^5 \)[/tex]:
[tex]\[ 1 \,405.6 \times 10^4 = 1.4056 \times 10^5 \][/tex]
Step 3: Adding the areas together:
Now, we add the areas of the South China Sea and the Arctic Ocean (both in [tex]\( 10^5 \)[/tex] km²):
[tex]\[ 8 \,003 \times 10^5 \, \text{km}² + 1.4056 \times 10^5 \, \text{km}² \][/tex]
This equals:
[tex]\[ 8 \,003 + 1.4056 = 9 \,408.6 \][/tex]
So, the combined area is:
[tex]\[ 9 \,408.6 \times 10^5 \, \text{km}² \][/tex]
Step 4: Writing the final answer in correct scientific notation with proper significant digits:
- The final result in scientific notation is [tex]\( 9.4086 \times 10^5 \)[/tex] km².
Therefore, the total area of the South China Sea and the Arctic Ocean combined is:
[tex]\[ 9.4086 \times 10^5 \, \text{km}². \][/tex]
