This is a “learning” quiz because every question has a “rule” or “clue” that accompanies it.
If you take your time and apply each rule to its corresponding question, it will be possible to “figure out” the correct answer to every question.
Let’s start with large numbers. To write a large number in scientific notation, we first have to move the decimal point to a number between 1 and 10.
Since moving the decimal point changes the value, we have to apply multiplication by the power of 10 that will yield an equivalent value to the original.
To figure out the exponent, we just count the number of places we moved the decimal sideways. That number is the exponent for the power of 10.
The process for moving between decimal and scientific notation is the same for small numbers (between 0 and 1), but in this case, the decimal moves to the right and the exponent will be negative.