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

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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:

$47.008 xx 10^2 =>$

$4.7008 xx 10^3$

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