#(8xx10^-7)(2xx10^5)#?

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scientific notation

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Answer 1 · 2017-10-23T01:51:15

The answer of this calculation is #1.6 xx 10^-1#

When multiplying numbers in scientific notation, first you multiply the whole numbers.

In this case, they are #8 and 2#, which equals #16. #

Then for the exponents: when multiplying, you add the exponents. So that would be # -7 +5 = -2#.

We have #16 xx 10^-2#.

But in scientific notation, there must be only ONE digit before the decimal point.

#16 xx 10^-2 = 1.6 xx10^-1#

In decimal notation the answer is #0.16#

Answer 2 · 2017-10-25T12:08:35

#=16 xx 10^-2 = 1.6 xx 10^-1#

Multiplying in scientific notation can be compared to multiplying in algebra:

#3x^4 xx 5x^3# can also be written as:

#color(red)(3xx5) xx color(blue)(x^4 xx x^3)#

#= color(red)(15) xx color(blue)(x^(4+3)" "larr# bases are both #x#, so add the indices

#= color(red)(15) xx color(blue)(x^7)#

In scientific notation you might have:

#3xx 10^8 xx 4 xx 10^11#

#= color(red)(3xx4) xx color(blue)(10^8 xx 10^11)#

#= color(red)(12) xx color(blue)(10^19)#

However in scientific notation, there must be one digit before the decimal point:

#color(red)(12) xxcolor(blue)(10^19) = color(red)(1.2) xx color(blue)(10^20)#

In this example we have:

#8 xx 10^-7 xx 2xx10^5#

#= color(red)(8 xx2) xx color(blue)(10^-7 xx10^5)#

#=color(red)(16) xx color(blue)(10^(-7+5))#

#=color(red)(16) xx color(blue)(10^-2)#

However in scientific notation, there must be one digit before the decimal point:

#=color(red)(16) xx color(blue)(10^-2) = color(red)(1.6) xx color(blue)(10^-1)#

It is usual to give an answer in the same format as the question.

In decimal format this answer would be #0.16#