How do you express #90000/0.03# in scientific notation and then divide using the rules of exponents?

Question

Julia Adams · Accepted Answer

#3*10^6#

In scientific notation, you have #90000 = 9*10^4# and #0.03=3*10^(-2)#. The fraction becomes

#\frac{9*10^4}{3*10^(-2)}#

We can simplify the numeric and exponential parts separately, so we can begin with

#\frac{cancel(9)^3*10^4}{cancel(3)*10^(-2)} = \frac{3*10^4}{10^(-2)}#

As for the exponential part, we use the definitions

#a^b*a^c = a^(b+c)#

#a^b/a^c = a^(b-c)#

to conclude that

#\frac{3*10^4}{10^(-2)} = 3*10^{4-(-2)} = 3*10^6#

Ethan Adkins · Answer

#3.0xx10^6#

Given: #90000/0.03#

#color(brown)(" Both methods")#

#color(blue)("Without the rules of exponents for comparison")#

Lets get rid of the decimal.

#90000/0.03xx1 color(white)("d")->color(white)("d")90000/0.03xx100/100 =9000000/3#

Giving: #3000000 =3.0xx10^6# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Using rules of exponents")#

#color(purple)(90000/0.03 color(white)("d") = color(white)("d")(9xx10^4)/(3xx10^(-2))color(white)("d") =color(white)("d") 9/3xx(10^4)/(10^(-2)))#

but #1/(10^("negative 2")) = 10^("positive 2")# giving:

#color(purple)(9/3xx10^(4+2)=3.0xx10^6)#

Abigail Allen · Answer

undefined 9.0 x 10^6

To divide using the rules of exponents, you subtract the exponent of the divisor from the exponent of the dividend:
(9.0 x 10^6) / (3 x 10^-2) = (9.0 / 3) x 10^(6 - (-2)) = 3.0 x 10^8