# How do you express the product of (35,000)(.00046) in scientific notation?

Mar 29, 2015

First you write both numbers in scientific notation

$35000 = 3.5 \cdot {10}^{4}$
because you have to move the decimal point 4 places to the left to leave one non-zero digit in front of the decimal point

$0.00046 = 4.6 \cdot {10}^{-} 4$
decimal point 4 to the right to get one one-zero digit in front of the decimal point (remember: to the right means negative $10$-power)

Now you multiply the numbers and add the $10$powers:

$3.5 \cdot 4.6 = 16.1$ and $4 + \left(- 4\right) = 0$

So the initial answer is $16.1 \cdot {10}^{0}$
But we now have two non-zero numbers before the decimal point,so:
$16.1 \cdot {10}^{0} = 1.61 \cdot {10}^{1}$ (move one to the left)