Question

Could someone help me? the video doenst explain it

Answer 1

Personally, I would recommend reading this as a fraction, and splitting up mantissa from the power of 10. (Mantissa refers to the number 1.23 in $1.23\times10^n$.)

$\left(3.6 \times 10^{-5}\right) \div \left(9 \times 10^{-7}\right) = \dfrac{3.6 \times 10^{-5}}{9 \times 10^{-7}} = \dfrac{3.6}9 \times \dfrac{10^{-5}}{10^{-7}}$

Now just reduce each fraction:

$\dfrac{3.6}9 = \dfrac{36}{90} = \dfrac25 = 0.4$

$\dfrac{10^{-5}}{10^{-7}} = 10^{-5-(-7)} = 10^{-5+7} = 10^2$

So

$\left(3.6 \times 10^{-5}\right) \div \left(9 \times 10^{-7}\right) = 0.4 \times 10^2 = \boxed{4 \times 10^1}$

since $0.4\times10^2 = 0.4 \times 100 = 40 = 4 \times 10$.