Question

What is 5,435,778 expressed in scientific notation? A. 5.435778 x 10 B. 5.435778 x 10 C. 5.435778 x 10 D. 5.435778 x 10

Answer 1

The answer options seem to be missing their exponents for the 10 unit.

Answer is: 5.435778 x
`10^(6)`

Explanation:

5,435,778

Move the decimal point to the left until it is between the 5 and 4. Scientific notation means rewriting the number with only one digit to the left of the decimal point and adding the "x
`10^(x)` after to account for the number of positions the decimal point was moved.

Count the number of places required for the move.

5,435,778 0

543577.8 1

54357.78 2

5435.778 3

543.5778 4

54.35778 5

5.435778 6

Each move reduces the number by a factor of 10. This means that the final move to make the number 5.435778 required dividing the original number by 10 a total of 6 times. By multiplying this last number by 10 a total of 6 times, we obtain the original number.

We could write this as: (5.435778)*(10)*(10)*(10)*(10)*(10)*(10)

but that defeats the purpose of scientific notation, which is to simplify the number so that it is 1) easier to read, 2) saves printers paper and ink, and 3) reduces transcription errors.

So scientific notation is the process of writing this as:

5.435778 x
`10^(6)`