# How do you write 400 in exponential notation?

Jan 12, 2017

See explanation.

## $400 = 4 \times {10}^{2}$

To write a number in scientific (exponential) notation you "move" the decimal point until you get a number between 1 and 10 and multiply this number by 10 raised to the power equal to the number of "moves" if the original number was greater than 10 or opposite to this number if the original number was lower than 1.

Example 1.

To write 425000 in scientiffic notation:

step 1: the number between 1 and 10 is: $4.25$
step 2: the number of "moves" is $5$ and the point was moved left, so the exponent is $5$ (plus five)
finally: $425 , 000 = 4.25 \times {10}^{5}$

Example 2.

To write $0.00023$:

step 1: The number between $1$ and $10$ is $2.3$
step 2: The number of "moves" is $4$ and the point was moved right, so the exponent is $- 4$ (minus four)
finally: $0.00023 = 2.3 \times {10}^{- 4}$