Question

largest number that can go into 6.022 x 10^23 without changing it

Answer 1

yes, i know that but i need to find the largest number to go into it with out changing the 6.022 * 10^23 form.

Answer 2

1?

Answer 3

or 1X10^0?

Answer 4

1 is the only thing that will go into anything without changing it, except zero.

Answer 5

the largest number you can add to it.

Answer 6

1.00X10^0

Answer 7

9?

Answer 8

In chemistry, 6.022× 1023 is an important number called the Avogadro constant (or Avogadro\'s number). It expresses the number of atoms or molecules in a mole. Notice that it is a really, really big number, as indicated by scientific notation with a large positive exponent. Enter 6.022× 1023 into the calculator shown here. Then, by trial and error, find the largest number that can be added to 6.022× 1023 without changing its displayed value (as shown on the screen).

Answer 9

6.22X10^23=622000000000000000000000 (+9) = 6220000000000000000000009, or 6.22X10623+ hmmmm... 1.0X10^21?

Answer 10

6.022* 10^23 not 0.022 X 1023

Answer 11

yeah, so you're learning about sig figs?

Answer 12

so you have how many sig figs?

Answer 13

3?

Answer 14

uhm, I think that looks like 4, personally. I could be wrong.

Answer 15

6.022

Answer 16

i meant 4

Answer 17

so now you need to know how take that 6.022 to 6.0224

Answer 18

because, that would keep your sig figs at 6.022 right?

Answer 19

I have no idea to be honest.

Answer 20

so you need something that starts with a 4 and has a lot of 9's after it (because it's the highest number that will not change your 4 sig figs.

Answer 21

99999999999999 goes into it without changing but it isnt the correct answer.

Answer 22

so tell me, how would you express 6.02249999999999999999999 in scientific notation?

Answer 23

to 4 sig figs, that is

Answer 24

6.022 * 10^23

Answer 25

I would write 6.022x10^23 b/c you can't round up to 6.023... because the number after your 4th sig fig is a 4

Answer 26

I am so confused.

Answer 27

if i would add the to the problem it would change it.

Answer 28

ha ha so if I said, round 6022.49 to 4 significant figures, what would you write?

Answer 29

6022

Answer 30

yeah, that's what I would write. I am assuming if I gave you the same question with the numbers 6022.50000001, you'd write something different?

Answer 31

what

Answer 32

you'd round that up to 6023

Answer 33

I would

Answer 34

so what I am thinking, is that your number is 4.99x10^x

Answer 35

why x?

Answer 36

well, the x is for you to figure out!

Answer 37

you've made me more confused than I already was :/

Answer 38

I don't want to answer it for you, I want to put you on the right track

Answer 39

I am sorry, so you want to add some number to 6.022X10^23, without changing that. So in order to do that, you need to think of the highest possible number that you would add that would NOT affect how you'd round that figure of 6.022x10^23. if you had 6.0225X10^23, you'd have to express that as 6.023X10^23 if you only could use 4 sig figs

Answer 40

BUT, if you had 6.0224X10^23, and you had to write it with only 4 sig figs, you would write 6.022x10^23, right?

Answer 41

Maybe I should back up, are you learning significant figures in chemistry right now, is that what this problem is?

Answer 42

I am assuming so. Im sorry but I am so confused and Yes, I am.

Answer 43

well we are suppose to be learning it, but my teacher didnt really teach anything of it beside the definition.

Answer 44

okay, fair enough. So if the problem gives you 6.022X10^23, they want the answer with 4 significant figures, in this case they want 6.022. Now, they want you to NOT change the number at all, and that includes the exponent, so they want 6.022X10^23 to be expressed exactly as is.

Answer 45

They are asking, what is the highest possible value that you can have, and still express the number as 6.022X10^23

Answer 46

but if you add something, you change the number am i mistaken

Answer 47

so you need to find the number that is 1 less than the lowest number that would force you to round up. If that number (the lowest one that would force you to change your written number) is 5.0X10^20, which would equal 6.0225X10^23, or 6.023X10^23(with 4 sig figs), you need to subtract 1 from that.

Answer 48

yes, you change the value, but we are rounding!

Answer 49

if your sales tax is 8.25% on $1, can you pay $1.0825? Nope, you have to round it, so the cashier says your total is $1.08. In that case, the highest sales tax that would make you still pay $1.08 is 8.49%, because the cashier still HAS to round down.

Answer 50

i feel like a complete idiot right now.

Answer 51

This is the exact same concept. 6.022499999...X10^23 is the answer. Expressed as scientific notation, that would be 4.9X10^19, I think.

Answer 52

Don't! I'm probably just not explaining it well. I will try again.

Answer 53

round 9.5 to the nearest whole number for me.

Answer 54

10

Answer 55

round 10.4 to the nearest whole number for me.

Answer 56

10

Answer 57

two different values, yet still the same answer, yes?

Answer 58

yes

Answer 59

what is the maximum number I can add to 10 that, rounding, will still give me 10?

Answer 60

4

Answer 61

nope, that would give you 14

Answer 62

because if its 5 you round up

Answer 63

.4

Answer 64

yup!

Answer 65

now if I asked for the highest number to 10 decimal places that would still leave me with 10, you'd say 10.4999999999, right?

Answer 66

no because the .4 would round up to 5 making it 11?

Answer 67

it would make its 10.5 which is considered 11

Answer 68

ohh, that's good logic! but if you think about it in whole values, you'd say your threshold for rounding up or down is 50%, so if I have 49.99999%, I have LESS than 50%, so I can't round up.

Answer 69

but that does round up to 50 because of the .999999

Answer 70

Sure, I could round 49.999 to 50, but because I have less than 50, I can't round 5.499999 to 5.50, because that second 5 is not really five, it's a 4 with a bunch of 9's after it.

Answer 71

Yup! the 4.99999 rounds up to 5.0, but the 5.49999999 does not round up to 6. It rounds up to 5.5

Answer 72

okay.

Answer 73

ionly round one number, not both.

Answer 74

so how could 10.499999999 round up to 11? It could round up to 10.5, but we are looking for just whole numbers in my example

Answer 75

Yes, because you are more than half of the whole number off! .499999 < half

Answer 76

yes, I understand what you are saying. We are rounding to the nearest tenth, not whole. correct?

Answer 77

yes, so if I asked to round to the nearest whole, you couldn't make that jump because you don't have enough (money, weight, pencils, etc) to say that.

Answer 78

correct.

Answer 79

so, what's the most I could add to 6.022X10^23 that would STILL leave me with 6.022X10^23?

Answer 80

probably 6.022499999999...., that would round to 6.0225, but not to 6.023!

Answer 81

make sense?

Answer 82

kinda

Answer 83

okay, so if you had $.499999 in the bank do you think the bank would let you withdraw $1? I mean, why not, you could round it up to $.50, and they'd probably let you withdraw $.50, but they'd NEVER let you round that up to $1, you don't even have half of a dollar!

Answer 84

ohh! I understand that.

Answer 85

now apply that to Avogadro's number and see what you get!

Answer 86

so take 6.022 *10^23 plus 4.99999999?

Answer 87

no thats not right.

Answer 88

well, that last 2 is what you want to add your 4.9999 to but it's such a large number that you'd probably think of it as 49999.... count the 9's write it as 4.99X10^x where x=the number of 9's you've counted.

Answer 89

4.99 * 10^14

Answer 90

so 6.022x10^23 has 23 numbers (21 of them are zeros) before the decimal point, if you were to write that number out. 6.022X10^23 = 602200000000000000000000

Answer 91

am I even close?

Answer 92

499999999999999+602200000000000000000000=?

Answer 93

not that correct answer.

Answer 94

remember, you're trying to get to 6.02249999999999999999999, right?

Answer 95

+0.0004999999?

Answer 96

+0.000049X10^23, yes, because with scientific notation you can't express the 9's after your last sig fig.

Answer 97

four 0000 not three?

Answer 98

0.000049 * 10^23 would be my answer?