Question

Avogadro’s number NA is 6.023 * 10^23. A sandpit contains 3.0115 billion sand grains. This corresponds to what fraction of NA?

How do I think:

Since I need to find a fraction, I can make a proportion:

Avagardo number/1=number of saind grains/x

Do I think correctly?

Answer 1

@phi

Answer 2

if the question, was "1 is what fraction of 10?" do you see the answer is 1/10

3 is what fraction of 6: 3/6 = ½

Answer 3

so I need to ignore the 10^12 and 10^23? if yes, how to write this correctly 'in math language'?

Answer 4

If we use your idea
\[ \frac{NA}{1}= \frac{sand}{x} \]
and solve for x, we get
\[ x = \frac{sand}{NA} \]
which is the same idea...
you want
\[ \frac{3.0115 \ billion}{6.023 \cdot 10^{23} }\]

Answer 5

I still don't get where 10^12 and 10^23 disappear : (

Answer 6

they don't disappear. billion is another name for \( 10^9\)
see https://en.wikipedia.org/wiki/Names_of_large_numbers

that means your fraction is
\[ \frac{3.0115 \cdot 10^9}{6.023 \cdot 10^{23} } \]

Answer 7

yeah, but I get 1/2 *10-14 is this an answer?

Answer 8

10^9 is 10*10*10*10*10*10*10*10*10*10= 1000000000
when you divide it by 10^23 (10 with 23 zeros) you get 10^14 in the bottom
\[ \frac{3.0115}{6.023 \cdot 10^{14}}\]

Answer 9

or I think correctly it should be 2*10^13, but is this a fraction?

Answer 10

and thanks;))

Answer 11

yes you get 0.5 * 10^-14
that is not in standard form (you want the lead number to be between 1 and 10)
so multiply the 0.5 * 10 and divide the 10^-14 by 10 (that keeps things balanced)
you get
5 * 10^-15

Answer 12

thanks: ))

Answer 13

and are you sure it is 5, not 2?

Answer 14

we start with
\[ \frac{3.0115 \ billion}{6.023 \cdot 10^{23} } \]
\[ \frac{3.0115 \cdot 10^9}{6.023 \cdot 10^{23} } \]
\[ \frac{3.0115}{6.023 \cdot 10^{14} } \]
\[ \frac{3.0115}{6.023} \cdot 10^{-14} \]
the 3.0115/6.023 = ½
\[ \frac{1}{2} \cdot 10^{-14} \]
change ½ to a decimal 0.5
\[ 0.5 \cdot 10^{-14} \]

now adjust 0.5 by multiplying by 10 (and divide by 10)
\[ 0.5 \cdot 10 \cdot 10^{-1} \cdot 10^{-14} \]
simplify that to
\[ 5.0 \cdto 10^{-15} \]

Answer 15

*\[ 5.0\cdot 10{−15} \]

Answer 16

okay, why do we need to change from 1/2 to decimal form?

Answer 17

you can write numbers lots of different ways, but math is confusing enough if people don't agree on a few standards.

Answer 18

and we can't simply just write 1/2 as 2, becase you need to change spmething with 10^-14, yeah?

Answer 19

you agree ½ of a pie is not the same as 2 pies ?
in other words ½ and 2 are not the same thing.

however, ½ and 0.5 are the same number. (as a fraction and as a decimal)

Answer 20

ywah, finally I DO understand: )) thanks again

Answer 21

but once you write the number as
0.5 * 10^-14 you are still not quite done...
0.5*10 = 5.0
and 10^-14 / 10 = 10^-15

and the answer in standard form is
\[ 5.0 \cdot 10^{-15} \]