# How do you write 0.000419 in scientific notation?

Apr 12, 2018

$4.19 \cdot {10}^{- 4}$

#### Explanation:

Scientific notation is always written as $a \cdot {10}^{b}$ where $a$ must be between $1$ and $10$.

You can see that we must multiply $0.00419$ by $10$ a total of four times (count out the number of spaces the decimal moves to the right). You need to make sure that the decimal is between the first positive integer, $4$ and the next one $9$.

However, if you multiplied the original number by ${10}^{4}$ to get $4.19$, you must balance it by multiplying it by the same amount.

$4.19 \cdot {10}^{- 4}$ is your answer.

Apr 12, 2018

$4.19 \cdot {10}^{-} 4$

#### Explanation:

To Get the Answer:
1. The number in front of the decimal point must be one digit and between 1 and 9 (including 1 and 9).
2. The numbers behind the decimal point two digits
3. Count the number of times the decimal point move from the original spot to the new spot, and it is times (X) 10 to the power of the amount of times it moved (X${10}^{n}$). NOTE: a) If the decimal point move backwards (right) then it is to the negative(-) power. b) If the decimal point move forward (left) then it is to the positive power.

Eg, 0.000419 => 4.19 X ${10}^{-} 4$ the number of times the decimal place moved in this case is 4 times backward.
Eg. 41900 => 4.19 X ${10}^{4}$ the number of times the decimal point moved in this case is 4 times forward.