This blog is the online extension of our intermediate classrooms. Our goal is to enhance and document our learning experience throughout the school year, and share this journey with teachers, parents and students. We welcome your constructive feedback, and we look forward to learning with you!
Basically, all you need to do is find the amount of numbers there are in each hundreds section. Since each time the hundreds value increases by 1, this means that there would be less possible numbers each time. For example, maximum for the 100s is 190, while the maximum for the 200s is 280. There is 10 1s, and 9 2s, which gives you 10+9+8+7+6+5+4+3+2+1 = 55.
From 100 to 999 there are 1000 possibilities, so the fraction would be 55/1000. BUT WAIT!!! 55/1000 is not reduced, so we reduce it to 11/200. BUT WEIGHT! We need to do it fractions, decimals, and percentages, so I divide 11 by 200. This gives me 0.055. The percentage would then be 5.5%. -Alan
There are 900 possibilities from 100 to 999 (those are the only three digit numbers equal to or past 100). 54 of them have their digits add up to ten. From 100 to 199 there are 10 possibilities (outcomes) that have their digits add to 10. 109, 118, 127, 136, 145, 154, 163, 172, 181, 190. From 200 to 299 there are 9. 208, 217, 226, 235, 244, 253, 262, 271, 280. It keeps going like this subtract 1 each time. So from 100 to 199, there's 10. 200 to 299, 9. 300 to 399, 8. 400 to 499, 7. 500 to 599, 6. 600 to 699, 5. 700 to 799, 4. 800 to 899, 3. 900 to 999, 2. That's all possibilities that when added up = 54.
54 over 900 possibilities is equivalent to 3 over 50 possibilities, 6 percent, and 0.06.
Therefore there are 54 numbers whose numbers equal 10 (from 100 to 999). The probability of the sum of the digits being equal to 10 is 54/900 (= 3/50). Percent: 6% Decimal: 0.06
Whoops, sorry for doing this late! So there are 900 possibilities. From 100-199 there are 10 numbers that their digits add up to 10. From 200-299 there are 9 numbers that their digits add up to 10. And so on, I realized this as I was doing this on paper so... 10+9+8+7+6+5+4+3+2=54 So 54/900 numbers have their digits add up to 10. Simplified: 3/50 Fraction: 3/50 Decimal: 0.06 Percent 6%
There are 900 different 3 digit integers that equal or are greater than 100, and when I looked at the numbers that added to 10, I realized that since the first digit was increasing with every 100, there would be 10 possibilities w/ numbers that started with 1, 9 that started with 2, and so on, so the amount of numbers that satisfy the conditions are 10+9+8+7+6+5+4+3+2+1/900, or 54/900 (3/50). Therefore, the probability of the sum of the digits of a number being 10 is 3/50, or 0.06 (6%).
Thank you to Alan who explained this question to me at school :DD The denominator is 900 and to figure out the numerator you add 10+9+8+7+6+5+4+3+2=54 because for each hundred, there will be one less number out of 900. 54/900 can be reduced to 3/50. Fraction: 3/50 Decimal: 0.06 Percent: 6%
Basically, all you need to do is find the amount of numbers there are in each hundreds section. Since each time the hundreds value increases by 1, this means that there would be less possible numbers each time. For example, maximum for the 100s is 190, while the maximum for the 200s is 280. There is 10 1s, and 9 2s, which gives you
ReplyDelete10+9+8+7+6+5+4+3+2+1 = 55.
From 100 to 999 there are 1000 possibilities, so the fraction would be 55/1000.
BUT WAIT!!!
55/1000 is not reduced, so we reduce it to 11/200.
BUT WEIGHT!
We need to do it fractions, decimals, and percentages, so I divide 11 by 200. This gives me 0.055.
The percentage would then be 5.5%.
-Alan
I'm pretty sure the "1" you added isn't supposed to be counted and anything under 100 isn't included making 900 possibilities instead of 1000.
DeleteYeah... MISCALCULATIONS ARE THE BEST.
DeleteIt's 54/900 which is 3/50, 0.06, and 6%. Thanks Seayrohn!
There are 900 possibilities from 100 to 999 (those are the only three digit numbers equal to or past 100). 54 of them have their digits add up to ten. From 100 to 199 there are 10 possibilities (outcomes) that have their digits add to 10. 109, 118, 127, 136, 145, 154, 163, 172, 181, 190. From 200 to 299 there are 9. 208, 217, 226, 235, 244, 253, 262, 271, 280. It keeps going like this subtract 1 each time. So from 100 to 199, there's 10. 200 to 299, 9. 300 to 399, 8. 400 to 499, 7. 500 to 599, 6. 600 to 699, 5. 700 to 799, 4. 800 to 899, 3. 900 to 999, 2. That's all possibilities that when added up = 54.
ReplyDelete54 over 900 possibilities is equivalent to 3 over 50 possibilities, 6 percent, and 0.06.
no problem
ReplyDeleteAmount of numbers from 100 to 999: 900
ReplyDeleteSmallest possible number (to add up): 109
...
127
136
145
154
163
172
181
190
However, each hundred will have one number less than the one before it.
100 - 199: 10
200 - 299: 9
300 - 399: 8
400 - 499: 7
500 - 599: 6
600 - 699: 5
700 - 799: 4
800 - 899: 3
900 - 999: 2
10+ 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 = 54
Therefore there are 54 numbers whose numbers equal 10 (from 100 to 999).
The probability of the sum of the digits being equal to 10 is 54/900 (= 3/50).
Percent: 6%
Decimal: 0.06
Whoops, sorry for doing this late! So there are 900 possibilities.
ReplyDeleteFrom 100-199 there are 10 numbers that their digits add up to 10.
From 200-299 there are 9 numbers that their digits add up to 10.
And so on, I realized this as I was doing this on paper so...
10+9+8+7+6+5+4+3+2=54
So 54/900 numbers have their digits add up to 10. Simplified: 3/50
Fraction: 3/50
Decimal: 0.06
Percent 6%
Grade 7 POTW
ReplyDeleteThere are 900 different 3 digit integers that equal or are greater than 100, and when I looked at the numbers that added to 10, I realized that since the first digit was increasing with every 100, there would be 10 possibilities w/ numbers that started with 1, 9 that started with 2, and so on, so the amount of numbers that satisfy the conditions are 10+9+8+7+6+5+4+3+2+1/900, or 54/900 (3/50). Therefore, the probability of the sum of the digits of a number being 10 is 3/50, or 0.06 (6%).
I agree with your final answer, but there isn't supposed to be a +1
DeleteAvi and Maxwell's POTW:
ReplyDeleteThe answer is 10+9+8+7+6+5+4+3+2+1 = 54.
Therefore, the probability of the sums of the digits that is equaled to 10 is 54/900, or 3/50.
why does everyone do this? you don't add the one
DeleteThank you to Alan who explained this question to me at school :DD
ReplyDeleteThe denominator is 900 and to figure out the numerator you add 10+9+8+7+6+5+4+3+2=54
because for each hundred, there will be one less number out of 900.
54/900 can be reduced to 3/50.
Fraction: 3/50
Decimal: 0.06
Percent: 6%
:DD