Question

Mental Arithmetic

Are there any tricks to solve the following problem, mentally. Not Using a calculator

3e-9 / 0.0015

Answer 1

\[\large \dfrac{3e^{-9}}{0.0015}\]

like that ?

Answer 2

or perhaps this
\[\large \dfrac{3\times 10^{-9}}{0.0015}\]

Answer 3

yeah thats right, how can u do that mentally?

Answer 4

3 x 10^-9 / 0.0015

Answer 5

@rational

Answer 6

The numerator is given in scientific notation. You convert the denominator in scientific notation. It will be easier to do without a calculator.

Answer 7

0.0015 is 15*10^(-4)
You have 3*10^(-9) divided to 15 * 10^(-4).

Divide 3 to 15 and 10*(-9) to 10^(-4) individually and multiply the two results.
Thus you have 1/5 which is 0.2 - multiplied with 10^(-5).

10^(-5) means just adding zero 5 times after the point and before the number, so the answer is :

0.000002 or 2*10^(-6)

I love mental math.

Answer 8

I would say 1.5 divides into 3 to give us 2
to get 1.5 in the bottom we multiply by 10^3. to compensate, we also multiply by 10^-3
\[ \dfrac{3\times 10^{-9}}{0.0015} = \\

\frac{3 \cdot 10^{-9}}{1.5 \cdot 10^{-3} }\]
thus we expect the answer to be 2 * 10^some_exponent
-9 - -3 = -9 +3 = -6
so
\[ 2 \cdot 10^{-6} \]
which you can do in your head if you are good at this sort of thing.