How do you simplify and write #(3.11times10^3)(1.01times10^13)# in standard form?

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Answer 1 · 2017-04-15T17:00:39

#3.1411 xx 10^16= 31,411,000,000,000,000. #

Consider the product: #" "3x^4 xx 5x^7#

This can also be written as #" "color(blue)(3 xx 5) xx color(red)(x^4 xx x^7)#

Multiply the numbers and add the indices of like bases.

#3x^4 xx 5x^7=color(blue)(15)color(red)(x^11)#

In the same way: #" "3.11 xx 10^3 xx1.01 xx 10^13#

Re-arrange to give: #" "color(blue)(3.11 xx1.01) xx color(red)(10^3 xx 10^13)#

Multiply the numbers and add the indices of like bases.

#=color(blue)(3.1411) xx color(red)(10^16)#

In some cases the number ends up as a number of 10 or more and has to be adjusted to be in scientific notation.

In decimal notation #3.1411 xx 10^16 = 31,411,000,000,000,000.#

#3.2 xx 10^8 xx 6.5 xx 10^11 = 20.8 xx 10^19 = 2.08 xx 10^20#