How do you write the answer in scientific notation given #((3.3times10^9)(2.8times10^-7))/(4.62times10^5)#?

2 Answers
Mar 21, 2017

Answer:

#2.0xx10^(-3)#

Explanation:

We do this in 3 parts:

The numbers

The powers of 10

The final adjustment so that there is only 1 digit to the left of the decimal point and that that digit is greater than 0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Step 1")#

#(3.3xx2.8)/4.62 = 2.0#

Note that step 3 not needed as there is only 1 digit non zero to right of decimal point.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Step 2")#

Note that #10^(-7) -> 1/10^7#

#10^9xx1/10^7xx1/10^5 =10^9/10^12 = 10^(9-12)=10^(-3)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#

#2.0xx10^(-3)#

Mar 21, 2017

Answer:

Igot: #2xx10^-3#

Explanation:

We can deal first with the powers of ten using the rule of exponents to get:
#10^9*10^-7/10^5=10^(9-7)/10^5=10^(2-5)=10^-3#
next we deal with the numbers:
#3.3xx2.8=9.24#
and
#9.24/4.62=2#
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so that we get:
#2xx10^-3#