How do you simplify #(9.04times10^6)(5.2times10^-4)#?

Question

1794 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-29T12:49:00

#4.7008xx10^3#

#9.04xx5.2=47.008#

#10^6xx10^(-4)=10^(6+ -4)=10^2#

#(9.04xx10^6)(5.2xx10^(-4))=47.008xx10^2#

#4.7008xx10^3#

Answer 2 · 2018-05-29T12:51:43

See a solution process below:

First, rewrite the expression as:

#9.04 xx 10^6 xx 5.2 xx 10^-4 =>#

#9.04 xx 5.2 xx 10^6 xx 10^-4 =>#

#(9.04 xx 5.2) xx (10^6 xx 10^-4) =>#

#47.008 xx (10^6 xx 10^-4)#

Next, multiply the two 10s terms using this rule for exponents:

#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#47.008 xx (10^color(red)(6) xx 10^color(blue)(-4) =>#

#47.008 xx 10^(color(red)(6) + color(blue)(-4)) =>#

#47.008 xx 10^(color(red)(6) - color(blue)(4)) =>#

#47.008 xx 10^2#

To put this expression into scientific notation we must move the decimal point one place to the left so we need to add 1 to the 10s exponent:

#47.008 xx 10^2 =>#

#4.7008 xx 10^3#