If the set $S$ consists of $900,000,000$ whole numbers, each with the same number of digits, how many digits are the numbers?
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I'm learning College Algebra myself. I have a topic as the following:
The set, S consists of 900,000,000 whole numbers, each being the same number of digits long. How many digits long is a number from S? (Hint: use the fact that a whole number cannot start with the digit 0.)
But I don't really understand "each being the same number of digits long". May anyone help me explain this part? I'll find the answer myself then. Thanks a lot!
combinatorics
edited Aug 24 at 19:06
N. F. Taussig
38.8k93153
asked Aug 23 at 9:46
Willy
122
add a comment |Â
up vote
0
down vote
favorite
I'm learning College Algebra myself. I have a topic as the following:
The set, S consists of 900,000,000 whole numbers, each being the same number of digits long. How many digits long is a number from S? (Hint: use the fact that a whole number cannot start with the digit 0.)
But I don't really understand "each being the same number of digits long". May anyone help me explain this part? I'll find the answer myself then. Thanks a lot!
combinatorics
edited Aug 24 at 19:06
N. F. Taussig
38.8k93153
asked Aug 23 at 9:46
Willy
122
Can you clarify what is a whole number? Perhaps an integer? I know because in Russian integer numbers literally translate as "whole"
– Aleksejs Fomins
Aug 23 at 9:51
Hi there. Whole number is natural number like 1,2,3,... except 0.
– Willy
Aug 23 at 9:53
The same number of digits long means that all of the numbers have the same number of digits. For instance, they could all have five digits such as $12345$, $27843$, and $30000$.
– N. F. Taussig
Aug 23 at 9:55
I think what is meant in the problem that all numbers in the set have the same number of digits. like 100 has 3 digits and 5432 has 4 digits. Also, if it is a set, all numbers in it should be different. That means, that all numbers have to have at least 900,000,000 digits. If it was smaller, it would not have been possible for them to be different. But it could also be larger than that
– Aleksejs Fomins
Aug 23 at 9:55
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I'm learning College Algebra myself. I have a topic as the following:
The set, S consists of 900,000,000 whole numbers, each being the same number of digits long. How many digits long is a number from S? (Hint: use the fact that a whole number cannot start with the digit 0.)
But I don't really understand "each being the same number of digits long". May anyone help me explain this part? I'll find the answer myself then. Thanks a lot!
combinatorics
edited Aug 24 at 19:06
N. F. Taussig
38.8k93153
asked Aug 23 at 9:46
Willy
122
I'm learning College Algebra myself. I have a topic as the following:
The set, S consists of 900,000,000 whole numbers, each being the same number of digits long. How many digits long is a number from S? (Hint: use the fact that a whole number cannot start with the digit 0.)
But I don't really understand "each being the same number of digits long". May anyone help me explain this part? I'll find the answer myself then. Thanks a lot!
combinatorics
edited Aug 24 at 19:06
N. F. Taussig
38.8k93153
asked Aug 23 at 9:46
Willy
122
edited Aug 24 at 19:06
N. F. Taussig
38.8k93153
edited Aug 24 at 19:06
N. F. Taussig
38.8k93153
edited Aug 24 at 19:06
N. F. Taussig
38.8k93153
38.8k93153
asked Aug 23 at 9:46
Willy
122
asked Aug 23 at 9:46
Willy
122
asked Aug 23 at 9:46
Willy
122
122
Can you clarify what is a whole number? Perhaps an integer? I know because in Russian integer numbers literally translate as "whole"
– Aleksejs Fomins
Aug 23 at 9:51
Hi there. Whole number is natural number like 1,2,3,... except 0.
– Willy
Aug 23 at 9:53
The same number of digits long means that all of the numbers have the same number of digits. For instance, they could all have five digits such as $12345$, $27843$, and $30000$.
– N. F. Taussig
Aug 23 at 9:55
I think what is meant in the problem that all numbers in the set have the same number of digits. like 100 has 3 digits and 5432 has 4 digits. Also, if it is a set, all numbers in it should be different. That means, that all numbers have to have at least 900,000,000 digits. If it was smaller, it would not have been possible for them to be different. But it could also be larger than that
– Aleksejs Fomins
Aug 23 at 9:55
add a comment |Â
Can you clarify what is a whole number? Perhaps an integer? I know because in Russian integer numbers literally translate as "whole"
– Aleksejs Fomins
Aug 23 at 9:51
Hi there. Whole number is natural number like 1,2,3,... except 0.
– Willy
Aug 23 at 9:53
The same number of digits long means that all of the numbers have the same number of digits. For instance, they could all have five digits such as $12345$, $27843$, and $30000$.
– N. F. Taussig
Aug 23 at 9:55
I think what is meant in the problem that all numbers in the set have the same number of digits. like 100 has 3 digits and 5432 has 4 digits. Also, if it is a set, all numbers in it should be different. That means, that all numbers have to have at least 900,000,000 digits. If it was smaller, it would not have been possible for them to be different. But it could also be larger than that
– Aleksejs Fomins
Aug 23 at 9:55
Can you clarify what is a whole number? Perhaps an integer? I know because in Russian integer numbers literally translate as "whole"
– Aleksejs Fomins
Aug 23 at 9:51
Can you clarify what is a whole number? Perhaps an integer? I know because in Russian integer numbers literally translate as "whole"
– Aleksejs Fomins
Aug 23 at 9:51
Hi there. Whole number is natural number like 1,2,3,... except 0.
– Willy
Aug 23 at 9:53
Hi there. Whole number is natural number like 1,2,3,... except 0.
– Willy
Aug 23 at 9:53
The same number of digits long means that all of the numbers have the same number of digits. For instance, they could all have five digits such as $12345$, $27843$, and $30000$.
– N. F. Taussig
Aug 23 at 9:55
The same number of digits long means that all of the numbers have the same number of digits. For instance, they could all have five digits such as $12345$, $27843$, and $30000$.
– N. F. Taussig
Aug 23 at 9:55
I think what is meant in the problem that all numbers in the set have the same number of digits. like 100 has 3 digits and 5432 has 4 digits. Also, if it is a set, all numbers in it should be different. That means, that all numbers have to have at least 900,000,000 digits. If it was smaller, it would not have been possible for them to be different. But it could also be larger than that
– Aleksejs Fomins
Aug 23 at 9:55
I think what is meant in the problem that all numbers in the set have the same number of digits. like 100 has 3 digits and 5432 has 4 digits. Also, if it is a set, all numbers in it should be different. That means, that all numbers have to have at least 900,000,000 digits. If it was smaller, it would not have been possible for them to be different. But it could also be larger than that
– Aleksejs Fomins
Aug 23 at 9:55
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
2
down vote
First off, if you copied the question to the letter, it is a bad question. Did you change the phrasing or leave anything out?
Let's do a bit of a smaller example. Suppose that the number was 90 rather than 900,000,000. Then you will note that the 90 numbers
$$
10, 11, 12, 13, 14, 15, ldots, 97, 98, 99
$$
all have exactly 2 digits. So if your set consists of these 90 numbers, then the correct answer is 2. This is also presumably the intended answer to the question (at least if you replace 900,000,000 with 90).
(Note that the numbers "$01, 02, 03, ldots, 09$" don't count: for the purposes of this question, numbers do not have leading zeroes, so these numbers should be written "$1, 2, 3, ldots, 9$" and therefore have 1 digit, not 2.)
However, the 90 numbers
$$
110, 111, 112, ldots, 197, 198, 199
$$
all have exactly 3 digits. So your set could consist of these 90 numbers as well, and then the answer would be 3. Because the question (as you wrote it) doesn't specify that the set $S$ should contain all numbers with that number of digits. If you add that condition, then the answer to the modified question is unequivocally 2.
Can you do the question for the number 900,000,000 (instead of 90) yourself?
answered Aug 23 at 9:55
Mees de Vries
14k12348
2
Firstly, thank all of you, nice people! I understood the problem. Here how i solve it using Multiplication Principal: - first digit takes 1 -> 9. From the second digit on, they take 0 -> 9. So I have equation: 9x10^n = 900 000 000 <=> n = 8 => a number from S has (8+1) digits
– Willy
Aug 23 at 10:21
@Willy, that's exactly right!
– Mees de Vries
Aug 23 at 10:45
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
First off, if you copied the question to the letter, it is a bad question. Did you change the phrasing or leave anything out?
Let's do a bit of a smaller example. Suppose that the number was 90 rather than 900,000,000. Then you will note that the 90 numbers
$$
10, 11, 12, 13, 14, 15, ldots, 97, 98, 99
$$
all have exactly 2 digits. So if your set consists of these 90 numbers, then the correct answer is 2. This is also presumably the intended answer to the question (at least if you replace 900,000,000 with 90).
(Note that the numbers "$01, 02, 03, ldots, 09$" don't count: for the purposes of this question, numbers do not have leading zeroes, so these numbers should be written "$1, 2, 3, ldots, 9$" and therefore have 1 digit, not 2.)
However, the 90 numbers
$$
110, 111, 112, ldots, 197, 198, 199
$$
all have exactly 3 digits. So your set could consist of these 90 numbers as well, and then the answer would be 3. Because the question (as you wrote it) doesn't specify that the set $S$ should contain all numbers with that number of digits. If you add that condition, then the answer to the modified question is unequivocally 2.
Can you do the question for the number 900,000,000 (instead of 90) yourself?
answered Aug 23 at 9:55
Mees de Vries
14k12348
2
Firstly, thank all of you, nice people! I understood the problem. Here how i solve it using Multiplication Principal: - first digit takes 1 -> 9. From the second digit on, they take 0 -> 9. So I have equation: 9x10^n = 900 000 000 <=> n = 8 => a number from S has (8+1) digits
– Willy
Aug 23 at 10:21
@Willy, that's exactly right!
– Mees de Vries
Aug 23 at 10:45
add a comment |Â
up vote
2
down vote
First off, if you copied the question to the letter, it is a bad question. Did you change the phrasing or leave anything out?
Let's do a bit of a smaller example. Suppose that the number was 90 rather than 900,000,000. Then you will note that the 90 numbers
$$
10, 11, 12, 13, 14, 15, ldots, 97, 98, 99
$$
all have exactly 2 digits. So if your set consists of these 90 numbers, then the correct answer is 2. This is also presumably the intended answer to the question (at least if you replace 900,000,000 with 90).
(Note that the numbers "$01, 02, 03, ldots, 09$" don't count: for the purposes of this question, numbers do not have leading zeroes, so these numbers should be written "$1, 2, 3, ldots, 9$" and therefore have 1 digit, not 2.)
However, the 90 numbers
$$
110, 111, 112, ldots, 197, 198, 199
$$
all have exactly 3 digits. So your set could consist of these 90 numbers as well, and then the answer would be 3. Because the question (as you wrote it) doesn't specify that the set $S$ should contain all numbers with that number of digits. If you add that condition, then the answer to the modified question is unequivocally 2.
Can you do the question for the number 900,000,000 (instead of 90) yourself?
answered Aug 23 at 9:55
Mees de Vries
14k12348
2
Firstly, thank all of you, nice people! I understood the problem. Here how i solve it using Multiplication Principal: - first digit takes 1 -> 9. From the second digit on, they take 0 -> 9. So I have equation: 9x10^n = 900 000 000 <=> n = 8 => a number from S has (8+1) digits
– Willy
Aug 23 at 10:21
@Willy, that's exactly right!
– Mees de Vries
Aug 23 at 10:45
add a comment |Â
up vote
2
down vote
up vote
2
down vote
First off, if you copied the question to the letter, it is a bad question. Did you change the phrasing or leave anything out?
Let's do a bit of a smaller example. Suppose that the number was 90 rather than 900,000,000. Then you will note that the 90 numbers
$$
10, 11, 12, 13, 14, 15, ldots, 97, 98, 99
$$
all have exactly 2 digits. So if your set consists of these 90 numbers, then the correct answer is 2. This is also presumably the intended answer to the question (at least if you replace 900,000,000 with 90).
(Note that the numbers "$01, 02, 03, ldots, 09$" don't count: for the purposes of this question, numbers do not have leading zeroes, so these numbers should be written "$1, 2, 3, ldots, 9$" and therefore have 1 digit, not 2.)
However, the 90 numbers
$$
110, 111, 112, ldots, 197, 198, 199
$$
all have exactly 3 digits. So your set could consist of these 90 numbers as well, and then the answer would be 3. Because the question (as you wrote it) doesn't specify that the set $S$ should contain all numbers with that number of digits. If you add that condition, then the answer to the modified question is unequivocally 2.
Can you do the question for the number 900,000,000 (instead of 90) yourself?
answered Aug 23 at 9:55
Mees de Vries
14k12348
First off, if you copied the question to the letter, it is a bad question. Did you change the phrasing or leave anything out?
Let's do a bit of a smaller example. Suppose that the number was 90 rather than 900,000,000. Then you will note that the 90 numbers
$$
10, 11, 12, 13, 14, 15, ldots, 97, 98, 99
$$
all have exactly 2 digits. So if your set consists of these 90 numbers, then the correct answer is 2. This is also presumably the intended answer to the question (at least if you replace 900,000,000 with 90).
(Note that the numbers "$01, 02, 03, ldots, 09$" don't count: for the purposes of this question, numbers do not have leading zeroes, so these numbers should be written "$1, 2, 3, ldots, 9$" and therefore have 1 digit, not 2.)
However, the 90 numbers
$$
110, 111, 112, ldots, 197, 198, 199
$$
all have exactly 3 digits. So your set could consist of these 90 numbers as well, and then the answer would be 3. Because the question (as you wrote it) doesn't specify that the set $S$ should contain all numbers with that number of digits. If you add that condition, then the answer to the modified question is unequivocally 2.
Can you do the question for the number 900,000,000 (instead of 90) yourself?
answered Aug 23 at 9:55
Mees de Vries
14k12348
edited Aug 23 at 9:59
answered Aug 23 at 9:55
Mees de Vries
14k12348
answered Aug 23 at 9:55
Mees de Vries
14k12348
answered Aug 23 at 9:55
Mees de Vries
14k12348
14k12348
2
Firstly, thank all of you, nice people! I understood the problem. Here how i solve it using Multiplication Principal: - first digit takes 1 -> 9. From the second digit on, they take 0 -> 9. So I have equation: 9x10^n = 900 000 000 <=> n = 8 => a number from S has (8+1) digits
– Willy
Aug 23 at 10:21
@Willy, that's exactly right!
– Mees de Vries
Aug 23 at 10:45
add a comment |Â
2
Firstly, thank all of you, nice people! I understood the problem. Here how i solve it using Multiplication Principal: - first digit takes 1 -> 9. From the second digit on, they take 0 -> 9. So I have equation: 9x10^n = 900 000 000 <=> n = 8 => a number from S has (8+1) digits
– Willy
Aug 23 at 10:21
@Willy, that's exactly right!
– Mees de Vries
Aug 23 at 10:45
2
2
Firstly, thank all of you, nice people! I understood the problem. Here how i solve it using Multiplication Principal: - first digit takes 1 -> 9. From the second digit on, they take 0 -> 9. So I have equation: 9x10^n = 900 000 000 <=> n = 8 => a number from S has (8+1) digits
– Willy
Aug 23 at 10:21
Firstly, thank all of you, nice people! I understood the problem. Here how i solve it using Multiplication Principal: - first digit takes 1 -> 9. From the second digit on, they take 0 -> 9. So I have equation: 9x10^n = 900 000 000 <=> n = 8 => a number from S has (8+1) digits
– Willy
Aug 23 at 10:21
@Willy, that's exactly right!
– Mees de Vries
Aug 23 at 10:45
@Willy, that's exactly right!
– Mees de Vries
Aug 23 at 10:45
add a comment |Â
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Can you clarify what is a whole number? Perhaps an integer? I know because in Russian integer numbers literally translate as "whole"
– Aleksejs Fomins
Aug 23 at 9:51
Hi there. Whole number is natural number like 1,2,3,... except 0.
– Willy
Aug 23 at 9:53
The same number of digits long means that all of the numbers have the same number of digits. For instance, they could all have five digits such as $12345$, $27843$, and $30000$.
– N. F. Taussig
Aug 23 at 9:55
I think what is meant in the problem that all numbers in the set have the same number of digits. like 100 has 3 digits and 5432 has 4 digits. Also, if it is a set, all numbers in it should be different. That means, that all numbers have to have at least 900,000,000 digits. If it was smaller, it would not have been possible for them to be different. But it could also be larger than that
– Aleksejs Fomins
Aug 23 at 9:55