How do you calculate #(1.025times10^4) + (9.814times10^5)#?

1 Answer
Apr 28, 2017

Answer:

#9.9165 * 10^5#

Explanation:

Here, you are taking two numbers that are in scientific notation and adding them.

#color(white)(aaaaaaaaaaa)(1.025×10^4)+(9.814×10^5)#

The thing to remember when adding in scientific notations is that you must have the base of 10 expressed with the same exponent.

So you #color(red)("CANNOT")# add the two together and get something like this

#color(white)(aaa)wrong->[(1.025×10^4)+(9.814×10^5) = 10.839 * 10^9]#

#---------------------#

To solve, you would have to change either the exponent in #(1.025×10^4) to 10^5 or (9.814×10^5) to 10^4#. We will do the former.

To change #(1.025×10^4)# in order to express the #"base 10"# as #10^5#, then using our little mnemonic,

#color(white)(aaaaaaaa)#I #color(red)("left it bigger")#, but you're #color(blue)("right, it's smaller")#

you would move the decimal point to the #color(red)("left")# of 1, moving it 1 time because to get from #4->5# you get #color(red)("bigger")# in value so you move left.

#color(white)(aaaaaaaa)(1.025×10^4)color(white)(aaaa)"becomes"color(white)(aaaa) (.1025*10^5)#

Now, add as normal.

#(.1025×10^5)+(9.814×10^5) = 9.9165 * 10^5#

Note: You do not do anything with the base #10^5#. You just have to express the scientific notations to have the same base and exponent in order to add at all