How do you multiply scientific notation $(0.33 x 10^{- 3}) x (0.2 x 10)$ $(0.33 x 10^ -3) x (0.2 x 10)$ ?

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Answer 1 · 2018-03-12T11:23:00

See a solution process below:

First, rewrite the expression as:

$(0.33 \times 0.2) \times (10^{- 3} \times 10) \Rightarrow$ $(0.33 xx 0.2) xx (10^-3 xx 10) =>$

$0.066 \times (10^{- 3} \times 10^{1})$ $0.066 xx (10^-3 xx 10^1)$

Next, use this rule of exponents to multiply the 10s terms:

$x^{a} \times x^{b} = x^{a + b}$ $x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))$

$0.066 \times (10^{- 3} \times 10^{1}) \Rightarrow$ $0.066 xx (10^color(red)(-3) xx 10^color(blue)(1)) =>$

$0.066 \times 10^{- 3 + 1} \Rightarrow$ $0.066 xx 10^(color(red)(-3)+color(blue)(1)) =>$

$0.066 \times 10^{- 2}$ $0.066 xx 10^-2$

To write this in scientific notation we must move the decimal point 2 places to the left so we need to subtract 2 from the 10s exponent:

$0.066 \times 10^{- 2} \Rightarrow$ $0.066 xx 10^-2 =>$

$6.6 \times 10^{- 4}$ $6.6 xx 10^-4$

How do you multiply scientific notation (0.33 x 10^ -3) x (0.2 x 10)(0.33x10−3)x(0.2x10)(0.33 x 10^ -3) x (0.2 x 10)?