How many micrograms are there in $2.45 \cdot 10^{3}$ $2.45*10^3$ grams?

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How many micrograms are there in $2.45 \cdot 10^{3}$ $2.45*10^3$ grams?

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Answer 1 · 2016-09-21T06:35:14

There are $2.45 \times 10^{9}$ $2.45xx10^9$ micrograms in $2.45 \times 10^{3}$ $2.45xx10^3$ grams .

Explanation:

$1$ $1$ microgram is one-millionth of standard unit, which is gram here,

Hence, one gram has $1, 000, 000$ $1,000,000$ or $10^{6}$ $10^6$ micrograms.

and $2.45 \times 10^{3}$ $2.45xx10^3$ grams are equivalent to $2.45 \times 10^{3} \times 10^{6} = 2.45 \times 10^{9}$ $2.45xx10^3xx10^6=2.45xx10^9$ micrograms.

Answer 2 · 2016-09-22T10:57:40

$micrograms = 2.45 \times 10^{3} \times 10^{6} = 2.45 \times 10^{9}$ $"micrograms "=2.45xx10^3xx10^6" "=" "2.45xx10^9$

Explanation:

$Establishing the ratio format and content$ $color(blue)("Establishing the ratio format and content")$

1 microgram $= 1 \times 10^{- 6} grams \leftarrow 1 millionth of 1 gram$ $= 1xx10^(-6)" grams " larr " 1 millionth of 1 gram"$
$.$ $color(white)(.)$

$Using ratio$ $color(red)("Using ratio")$

$\frac{micrograms}{grams} \to \frac{1}{10^{- 6}} \equiv \frac{micrograms}{2.45 \times 10^{3}}$ $("micrograms")/("grams") ->color(magenta)(1/(10^(-6))) -=("micrograms")/(2.45xx10^3)$

$.$ $color(white)(.)$

$but \frac{1}{10^{- 6}} is the same as \frac{10^{6}}{1}$ $color(red)("but "1/10^(-6) " is the same as "(10^6)/1)$

$.$ $color(white)(.)$

$\frac{micrograms}{grams} \to \frac{10^{6}}{1} \equiv \frac{micrograms}{2.45 \times 10^{3}}$ $("micrograms")/("grams") ->color(magenta)((10^6)/1) -= ("micrograms")/(2.45xx10^3)$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$The calculation$ $color(blue)("The calculation")$

$\frac{10^{6}}{1} \equiv \frac{micrograms}{2.45 \times 10^{3}}$ $color(brown)((10^6)/1 -=("micrograms")/(2.45xx10^3))$

$.$ $color(white)(.)$

$Multiply bot sides by 2.45 \times 10^{3}$ $color(red)("Multiply bot sides by "color(blue)(2.45xx10^3))$

$.$ $color(white)(.)$

$color(brown)((10^6)/1 color(blue)(xx2.45xx10^3) " "=" micrograms "xx(color(blue)(cancel(2.45xx10^3)))/(cancel(2.45xx10^3)) )$

$color(white)(.)$

$"micrograms "=2.45xx10^3xx10^6" "=" "2.45xx10^9$

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