How do you evaluate #0.028\times ( 3.4\times 10^ { 4} )#?

3 Answers
Mar 2, 2018

ANSWER; 952
Use BEDMAS; brackets, exponents, division/multiplication, addition/subtraction. (All in order)

Explanation:

-Begin with the brackets. Within the brackets, there is an exponent. Evaluate. It should give 10,000.

-Then multiply this number by 3.4 because it's in the brackets. You should get 34,000.

-Finish by multiplying this by 0.028. You should get 952

Mar 2, 2018

If the decimals are giving you a problem use the type of approach demonstrated.

#9.52xx10^2#

Explanation:

Lets get rid of the decimals for now and then put them back at the end

#3.4# is the same as #34xx1/10#

So #3.4xx10^4# is the same as #34xx1/10xx10^4 color(white)("dd") =color(white)("dd") 34xx10^3 #

#0.028# is the same as #28xx1/1000 = 28xx1/10^3#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#

#28xx1/10^3xx34xx10^3#

#28xx34xx10^3/10^3#

#28xx34 = 952#

Choosing to put this into the same format as in part of the question #(3.4xx10^4)# we have:

#952 ->9.52xx10^2#

Mar 2, 2018

Answer is #952#

Explanation:

#0.028 * (3.4 * 10^4)# Given Equation

First off, lets start with finding the value inside the brackets.
#3.4 * 10^4# In a way, this is just scientific notation, meaning that the number just by looking at it would be #34,000#.

However, if you are not familiar with scientific equation, you can first look at #10^4#. Well, what is #10 * 10 * 10 * 10#? It would be #10,000#.

Now that you have that part, we can continue looking inside the brackets. Giving us #3.4 * 10,000#. The way I would solve this is by, looking at the ONLY numbers that are not #0#.

So, really we are looking at #3.4 * 1#, which is #3.4#. Now we add the left over zeros, since #10,000# has a total of #4# zeros, add #4# zeros to #3.4#.

So #(3.4 * 10^4) = 34,000#. Great! Now to solve the rest.

#0.028 * 34,000# Is now leftover. Could solve this like a regular multiplication problem.

#34 * 28 = 952#, I would add the #3# zeros from #34,000#, however since #0.028# has #3# numbers behind the decimal point, that would cancel everything out. Making the answer be #952#.