Need help PnC | Mathematics | Page 1

misty aspen May 18, 2025, 8:36 AM

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The number of times the digit 3 will be written when listing the integers from 1 to 1000, is:

sharp spireBOT May 18, 2025, 8:36 AM

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misty aspen The number of times the digit 3 will be written when listing the integers from 1...

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strong perch May 18, 2025, 8:48 AM

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Think of it this way

misty aspen May 18, 2025, 8:48 AM

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Need help PnC

strong perch May 18, 2025, 8:48 AM

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How many times will it appear in the units place?

misty aspen May 18, 2025, 8:50 AM

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strong perch How many times will it appear in the units place?

Maybe 90?

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I was thinking

strong perch May 18, 2025, 8:51 AM

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misty aspen Maybe 90?

No
How many digits are there?

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In total

misty aspen May 18, 2025, 8:52 AM

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strong perch No How many digits are there?

10?

strong perch May 18, 2025, 8:52 AM

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Yes

misty aspen May 18, 2025, 8:52 AM

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0,1,2,3,4,5,6,7,8,9

strong perch May 18, 2025, 8:53 AM

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So 3 will come in the units place 1/…..

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It’s 10

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1/10th of the time

misty aspen May 18, 2025, 8:54 AM

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?

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how?

strong perch May 18, 2025, 8:54 AM

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misty aspen 10?

.

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All the digits are equally likely to be in the units place

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Now, what’s 1/10th of a 1000?

misty aspen May 18, 2025, 8:56 AM

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Why are we finding probability?

strong perch May 18, 2025, 8:56 AM

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misty aspen Why are we finding probability?

Just to find out how many times 3 comes in the units place

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Anyway, do the same thing for ten’s place

misty aspen May 18, 2025, 8:58 AM

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just wait a minute..

misty aspen May 18, 2025, 9:00 AM

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strong perch Anyway, do the same thing for ten’s place

1/9?

strong perch May 18, 2025, 9:00 AM

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No
It’s the same thing

misty aspen May 18, 2025, 9:01 AM

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1/10?

strong perch May 18, 2025, 9:01 AM

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So?

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How many times?

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1/10th of a 1000 is still 100

misty aspen May 18, 2025, 9:03 AM

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yes.

strong perch May 18, 2025, 9:03 AM

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So….?

misty aspen May 18, 2025, 9:04 AM

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same for hundredth place?

strong perch May 18, 2025, 9:05 AM

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So….?

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100, right?

misty aspen May 18, 2025, 9:05 AM

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yeah.

strong perch May 18, 2025, 9:05 AM

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So overall?

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How many times does it show up?

misty aspen May 18, 2025, 9:06 AM

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100*3

strong perch May 18, 2025, 9:06 AM

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Yep

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Good job

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You can use +close to close this thread if you’re done

misty aspen May 18, 2025, 9:07 AM

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wait

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I'm understanding it..

strong perch May 18, 2025, 9:08 AM

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Np

misty aspen May 18, 2025, 9:09 AM

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Can you help me to understand the book's solution?

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@strong perch

strong perch May 18, 2025, 9:10 AM

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What did the book do?

misty aspen May 18, 2025, 9:12 AM

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Number of times 3 occur= No. of numbers in which 3 occur at one place+2(No. of numbers in which 3 occur at two places)+3(No. of numbers in which 3 occur at three places)

strong perch May 18, 2025, 9:13 AM

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Well, yeah

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If a 3 comes up in a number once, you need to count it once

misty aspen May 18, 2025, 9:13 AM

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yes..

strong perch May 18, 2025, 9:13 AM

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If a 3 comes up in a number twice, you need to count it twice
If a 3 comes up in a number thrice, you need to count it thrice

misty aspen May 18, 2025, 9:15 AM

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And how to count that "No. of numbers in which 3 occur at three places"?

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ah got it on my own.

strong perch May 18, 2025, 9:16 AM

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misty aspen And how to count that "No. of numbers in which 3 occur at three places"?

There’s only 1

misty aspen May 18, 2025, 9:16 AM

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yeah, 333

strong perch May 18, 2025, 9:17 AM

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The breakdown is 243, 27, 1

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Btw

misty aspen May 18, 2025, 9:17 AM

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Using probability was actualy nice, i'm dumb that i couldn't found the solution on my own.

strong perch May 18, 2025, 9:17 AM

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misty aspen Using probability was actualy nice, i'm dumb that i couldn't found the solution ...

We all start somewhere

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It’s fine

misty aspen May 18, 2025, 9:18 AM

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strong perch We all start somewhere

Did you see that method in any book or you found it on your own?

strong perch May 18, 2025, 9:19 AM

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misty aspen Did you see that method in any book or you found it on your own?

On my own

misty aspen May 18, 2025, 9:19 AM

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woah, that's cool

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Thank you for the help.

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+close

fresh mantleBOT May 18, 2025, 9:19 AM

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misty aspen +close

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strong perch May 18, 2025, 9:19 AM

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Anytime

fresh mantleBOT May 18, 2025, 9:19 AM

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fresh mantle

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#Need help PnC