Multiply the decimal numbers:
5.3 x 4.2 = 22.26
When multiplying scientific numbers, add the exponents together: 4+3 = 7
So you now have 22.26 x 10^7
Now you need to convert 22.26 to a scientific number, by only having one number to the left of the decimal point.
You need to move the decimal 1 place to the left, which means you need to add 1 more to the exponent.
The final answer would be 2.226 x 10^8
