How do you evaluate $\frac{(3.00 \times 10^{6}) (2.0 \times 10^{- 3})}{5.0 \times 10^{- 2}}$ $\frac { ( 3.00\times 10^ { 6} ) ( 2.0\times 10^ { - 3} ) } { 5.0\times 10^ { - 2} }$ ?

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How do you evaluate $\frac{(3.00 \times 10^{6}) (2.0 \times 10^{- 3})}{5.0 \times 10^{- 2}}$ $\frac { ( 3.00\times 10^ { 6} ) ( 2.0\times 10^ { - 3} ) } { 5.0\times 10^ { - 2} }$ ?

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Answer 1 · 2016-12-10T14:33:27

$120, 000$ $120,000$ or $1.2 \times 10^{5}$ $1.2 xx 10^5$

Explanation:

First, rearrange the terms in the numerator:

$\frac{3.00 \times 2.0 \times 10^{6} \times 10^{- 3}}{5.00 \times 10^{- 2}}$ $(3.00 xx 2.0 xx 10^6 xx 10^-3)/(5.00 xx 10^-2)$

Using the rule for exponents where $x^{a} \times x^{b} = x^{a + b}$ $color(red)(x^a xx x^b = x^(a+b))$ we can simplify the numerator to:

$\frac{6.00 \times 10^{6 - 3}}{5.0 \times 10^{- 2}}$ $(6.00 xx 10^(6-3))/(5.0 xx 10^-2)$

$\frac{6.00 \times 10^{3}}{5.0 \times 10^{- 2}}$ $(6.00 xx 10^3)/(5.0 xx 10^-2)$

Now using the rule for exponents where $\frac{x^{a}}{x^{b}} = x^{a - b}$ $color(red)(x^a/x^b = x^(a-b))$ we can simplify the fraction to:

$\frac{6.00 \times 10^{(3 - - 2)}}{5.0}$ $(6.00 xx 10^((3 - -2)))/5.0$

$\frac{6.00 \times 10^{5}}{5.00}$ $(6.00 xx 10^5)/5.00$

Expanding the numerator gives us:

$\frac{600000}{5}$ $600000/5$

$120000$ $120000$

Or in scientific notation form:

$1.2 \times 10^{5}$ $1.2 xx 10^5$

Answer 2 · 2016-12-10T14:35:32

$1.2 \cdot 10^{5}$ $1.2 * 10^5$

Explanation:

$\frac{(3.00 \cdot 10^{6}) (2.0 \cdot 10^{- 3})}{5.0 \cdot 10^{- 2}}$ $((3.00 * 10^6)(2.0 * 10^-3))/(5.0 * 10^-2$

multiply out brackets:

$\frac{6.0 \cdot 10^{3}}{5.0 \cdot 10^{- 2}}$ $(6.0 * 10^3)/(5.0 * 10^-2)$

divide 6 by 5:

$\frac{1.2 \cdot 10^{3}}{10^{- 2}}$ $(1.2 * 10^3)/10^-2$

and then the powers of 10:

$1.2 \cdot 10^{5}$ $1.2 * 10^5$

(reason:) law of indices:
$(\frac{a^{m}}{a^{n}} = a^{m - n})$ $(a^m/a^n = a^(m-n))$

$1.2$ $1.2$ is between 1 and 10, so we do not need to change this or the power of 10.

final answer: $1.2 \cdot 10^{5}$ $1.2 * 10^5$

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How do you evaluate $\frac{(3.00 \times 10^{6}) (2.0 \times 10^{- 3})}{5.0 \times 10^{- 2}}$ $\frac { ( 3.00\times 10^ { 6} ) ( 2.0\times 10^ { - 3} ) } { 5.0\times 10^ { - 2} }$ ?

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How do you evaluate $\frac{(3.00 \times 10^{6}) (2.0 \times 10^{- 3})}{5.0 \times 10^{- 2}}$ $\frac { ( 3.00\times 10^ { 6} ) ( 2.0\times 10^ { - 3} ) } { 5.0\times 10^ { - 2} }$ ?