Is “three ten-millionths of an inch” the same as “thirty millionths of an inch”?
$begingroup$
I was reading this article when I came across a fraction that was difficult for me to comprehend:
three ten-millionths of an inch
I thought to myself that wouldn't this be the equivalent of:
thirty millionths of an inch
However, the thought then occurred to me that they must be two completely different values. The problem is that with the numbers being so small, I'm having a difficult time scaling this up to a bigger number that would make more sense ($frac{1}{3}$ for example).
Are the two phrases interchangeable, or am I correct in thinking they have two different values? How can each be represented with a larger fraction to ease comprehension?
fractions word-problem
edited Jan 15 at 23:24
Blue
48.3k870153
asked Jan 15 at 22:57
PerpetualJPerpetualJ
1787
$endgroup$
add a comment |
$begingroup$
I was reading this article when I came across a fraction that was difficult for me to comprehend:
three ten-millionths of an inch
I thought to myself that wouldn't this be the equivalent of:
thirty millionths of an inch
However, the thought then occurred to me that they must be two completely different values. The problem is that with the numbers being so small, I'm having a difficult time scaling this up to a bigger number that would make more sense ($frac{1}{3}$ for example).
Are the two phrases interchangeable, or am I correct in thinking they have two different values? How can each be represented with a larger fraction to ease comprehension?
fractions word-problem
edited Jan 15 at 23:24
Blue
48.3k870153
asked Jan 15 at 22:57
PerpetualJPerpetualJ
1787
$endgroup$
2
$begingroup$
It's not clear what you mean by thirty-millionths, because it doesn't make sense as it stands: you might mean thirty millionths (no hyphen!), that is 30/1 000 000; or one thirty-millionth, that is 1/30 000 000. (But neither of these is equal to three ten-millionths, that is 3/10 000 000.)
$endgroup$
– TonyK
Jan 15 at 23:08
$begingroup$
@TonyK Thank you for clarifying that point; I'll edit the post as it was unclear to me what the number was as well; but I would like to believe the first case of $frac{30}{1000000}$. I simply included the hyphen as I didn't understand the nature of its placement there.
$endgroup$
– PerpetualJ
Jan 15 at 23:12
2
$begingroup$
The issue is that the phrase 'a ten-millionth' is a bit misleading, or ambiguous at least, to someone unfamiliar with the terminology. It doesn't mean 'ten millionths'; it means 'a tenth of a millionth'. But you've interpreted it as the former. Just as millionth means 1/(a million), ten-millionth, i.e. (ten-million)th (not ten millionths), means 1/(ten million).
$endgroup$
– AlephNull
Jan 15 at 23:13
add a comment |
$begingroup$
I was reading this article when I came across a fraction that was difficult for me to comprehend:
three ten-millionths of an inch
I thought to myself that wouldn't this be the equivalent of:
thirty millionths of an inch
However, the thought then occurred to me that they must be two completely different values. The problem is that with the numbers being so small, I'm having a difficult time scaling this up to a bigger number that would make more sense ($frac{1}{3}$ for example).
Are the two phrases interchangeable, or am I correct in thinking they have two different values? How can each be represented with a larger fraction to ease comprehension?
fractions word-problem
edited Jan 15 at 23:24
Blue
48.3k870153
asked Jan 15 at 22:57
PerpetualJPerpetualJ
1787
$endgroup$
I was reading this article when I came across a fraction that was difficult for me to comprehend:
three ten-millionths of an inch
I thought to myself that wouldn't this be the equivalent of:
thirty millionths of an inch
However, the thought then occurred to me that they must be two completely different values. The problem is that with the numbers being so small, I'm having a difficult time scaling this up to a bigger number that would make more sense ($frac{1}{3}$ for example).
Are the two phrases interchangeable, or am I correct in thinking they have two different values? How can each be represented with a larger fraction to ease comprehension?
fractions word-problem
fractions word-problem
edited Jan 15 at 23:24
Blue
48.3k870153
asked Jan 15 at 22:57
PerpetualJPerpetualJ
1787
edited Jan 15 at 23:24
Blue
48.3k870153
asked Jan 15 at 22:57
PerpetualJPerpetualJ
1787
edited Jan 15 at 23:24
Blue
48.3k870153
edited Jan 15 at 23:24
Blue
48.3k870153
edited Jan 15 at 23:24
Blue
48.3k870153
48.3k870153
asked Jan 15 at 22:57
PerpetualJPerpetualJ
1787
asked Jan 15 at 22:57
PerpetualJPerpetualJ
1787
asked Jan 15 at 22:57
PerpetualJPerpetualJ
1787
1787
2
$begingroup$
It's not clear what you mean by thirty-millionths, because it doesn't make sense as it stands: you might mean thirty millionths (no hyphen!), that is 30/1 000 000; or one thirty-millionth, that is 1/30 000 000. (But neither of these is equal to three ten-millionths, that is 3/10 000 000.)
$endgroup$
– TonyK
Jan 15 at 23:08
$begingroup$
@TonyK Thank you for clarifying that point; I'll edit the post as it was unclear to me what the number was as well; but I would like to believe the first case of $frac{30}{1000000}$. I simply included the hyphen as I didn't understand the nature of its placement there.
$endgroup$
– PerpetualJ
Jan 15 at 23:12
2
$begingroup$
The issue is that the phrase 'a ten-millionth' is a bit misleading, or ambiguous at least, to someone unfamiliar with the terminology. It doesn't mean 'ten millionths'; it means 'a tenth of a millionth'. But you've interpreted it as the former. Just as millionth means 1/(a million), ten-millionth, i.e. (ten-million)th (not ten millionths), means 1/(ten million).
$endgroup$
– AlephNull
Jan 15 at 23:13
add a comment |
2
$begingroup$
It's not clear what you mean by thirty-millionths, because it doesn't make sense as it stands: you might mean thirty millionths (no hyphen!), that is 30/1 000 000; or one thirty-millionth, that is 1/30 000 000. (But neither of these is equal to three ten-millionths, that is 3/10 000 000.)
$endgroup$
– TonyK
Jan 15 at 23:08
$begingroup$
@TonyK Thank you for clarifying that point; I'll edit the post as it was unclear to me what the number was as well; but I would like to believe the first case of $frac{30}{1000000}$. I simply included the hyphen as I didn't understand the nature of its placement there.
$endgroup$
– PerpetualJ
Jan 15 at 23:12
2
$begingroup$
The issue is that the phrase 'a ten-millionth' is a bit misleading, or ambiguous at least, to someone unfamiliar with the terminology. It doesn't mean 'ten millionths'; it means 'a tenth of a millionth'. But you've interpreted it as the former. Just as millionth means 1/(a million), ten-millionth, i.e. (ten-million)th (not ten millionths), means 1/(ten million).
$endgroup$
– AlephNull
Jan 15 at 23:13
2
2
$begingroup$
It's not clear what you mean by thirty-millionths, because it doesn't make sense as it stands: you might mean thirty millionths (no hyphen!), that is 30/1 000 000; or one thirty-millionth, that is 1/30 000 000. (But neither of these is equal to three ten-millionths, that is 3/10 000 000.)
$endgroup$
– TonyK
Jan 15 at 23:08
$begingroup$
It's not clear what you mean by thirty-millionths, because it doesn't make sense as it stands: you might mean thirty millionths (no hyphen!), that is 30/1 000 000; or one thirty-millionth, that is 1/30 000 000. (But neither of these is equal to three ten-millionths, that is 3/10 000 000.)
$endgroup$
– TonyK
Jan 15 at 23:08
$begingroup$
@TonyK Thank you for clarifying that point; I'll edit the post as it was unclear to me what the number was as well; but I would like to believe the first case of $frac{30}{1000000}$. I simply included the hyphen as I didn't understand the nature of its placement there.
$endgroup$
– PerpetualJ
Jan 15 at 23:12
$begingroup$
@TonyK Thank you for clarifying that point; I'll edit the post as it was unclear to me what the number was as well; but I would like to believe the first case of $frac{30}{1000000}$. I simply included the hyphen as I didn't understand the nature of its placement there.
$endgroup$
– PerpetualJ
Jan 15 at 23:12
2
2
$begingroup$
The issue is that the phrase 'a ten-millionth' is a bit misleading, or ambiguous at least, to someone unfamiliar with the terminology. It doesn't mean 'ten millionths'; it means 'a tenth of a millionth'. But you've interpreted it as the former. Just as millionth means 1/(a million), ten-millionth, i.e. (ten-million)th (not ten millionths), means 1/(ten million).
$endgroup$
– AlephNull
Jan 15 at 23:13
$begingroup$
The issue is that the phrase 'a ten-millionth' is a bit misleading, or ambiguous at least, to someone unfamiliar with the terminology. It doesn't mean 'ten millionths'; it means 'a tenth of a millionth'. But you've interpreted it as the former. Just as millionth means 1/(a million), ten-millionth, i.e. (ten-million)th (not ten millionths), means 1/(ten million).
$endgroup$
– AlephNull
Jan 15 at 23:13
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
Don't confuse yourself.
Use simpler terms. "three quarters of an inch" means "$3times frac 14$ inch" or "$frac 3{4}$ inch".
It does not mean "one three$times$fourth" = "$frac 1{3times 4}=frac 1{12}$ inch"
Like wise "three ten-millionths of an inch" means "$3 times frac 1{10,000,000} = frac 3{10,000,000}$"
It does not mean $frac 1{3times 10,000,000} = frac {1 }{30,000,000}$.
answered Jan 15 at 23:15
fleabloodfleablood
70.1k22685
$endgroup$
$begingroup$
Now that actually explains it in extremely simple terms, thank you!
$endgroup$
– PerpetualJ
Jan 15 at 23:17
add a comment |
$begingroup$
They are different values, three ten-millionth is $frac{3}{10times 1000000} = 3cdot 10^{-7}$ and thirty-millionth is $frac{1}{30times 1000000}=3.bar{333}cdot 10^{-8}$.
answered Jan 15 at 23:04
Ori KainOri Kain
114
$endgroup$
$begingroup$
That should be three ten-millionths. In the context of this question, the distinction is important! And the OP didn't write thirty-millionth, but thirty-millionths, which is invalid. (But the question has now been edited, I see.)
$endgroup$
– TonyK
Jan 15 at 23:16
add a comment |
$begingroup$
Not the same.
Three ten-millionths would be (3/10 million) X 1 inch = 0.3 inches divided by 1 million. Thirty millionths of an inch would be 30 times an inch divided by 1 million. So they are different by two orders of magnitude.
I think 0.3 millionths of an inch would be the right description (not that it is any easier to comprehend...).
I think micro ($10^{-6}$), nano ($10^{-9}$), and pico ($10^{-12}$) come in really handy when dealing with small numbers. For example, 1 millionth of an inch can be called 1 micro-inch or 1 $mu$i. Then, 0.3 millionths of an inch becomes $0.3mu$i or 300 nano-inches.
answered Jan 15 at 23:06
Aditya DuaAditya Dua
1,11418
$endgroup$
$begingroup$
That should be three ten-millionths. And thirty-millionths is not the same as thirty millionths! A thirty-millionth is 1/30 000 000, but thirty millionths is 30/1 000 000.
$endgroup$
– TonyK
Jan 15 at 23:17
$begingroup$
Thanks @TonyK. Edited!
$endgroup$
– Aditya Dua
Jan 15 at 23:43
add a comment |
Your Answer
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3 Answers
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3 Answers
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$begingroup$
Don't confuse yourself.
Use simpler terms. "three quarters of an inch" means "$3times frac 14$ inch" or "$frac 3{4}$ inch".
It does not mean "one three$times$fourth" = "$frac 1{3times 4}=frac 1{12}$ inch"
Like wise "three ten-millionths of an inch" means "$3 times frac 1{10,000,000} = frac 3{10,000,000}$"
It does not mean $frac 1{3times 10,000,000} = frac {1 }{30,000,000}$.
answered Jan 15 at 23:15
fleabloodfleablood
70.1k22685
$endgroup$
$begingroup$
Now that actually explains it in extremely simple terms, thank you!
$endgroup$
– PerpetualJ
Jan 15 at 23:17
add a comment |
$begingroup$
Don't confuse yourself.
Use simpler terms. "three quarters of an inch" means "$3times frac 14$ inch" or "$frac 3{4}$ inch".
It does not mean "one three$times$fourth" = "$frac 1{3times 4}=frac 1{12}$ inch"
Like wise "three ten-millionths of an inch" means "$3 times frac 1{10,000,000} = frac 3{10,000,000}$"
It does not mean $frac 1{3times 10,000,000} = frac {1 }{30,000,000}$.
answered Jan 15 at 23:15
fleabloodfleablood
70.1k22685
$endgroup$
$begingroup$
Now that actually explains it in extremely simple terms, thank you!
$endgroup$
– PerpetualJ
Jan 15 at 23:17
add a comment |
$begingroup$
Don't confuse yourself.
Use simpler terms. "three quarters of an inch" means "$3times frac 14$ inch" or "$frac 3{4}$ inch".
It does not mean "one three$times$fourth" = "$frac 1{3times 4}=frac 1{12}$ inch"
Like wise "three ten-millionths of an inch" means "$3 times frac 1{10,000,000} = frac 3{10,000,000}$"
It does not mean $frac 1{3times 10,000,000} = frac {1 }{30,000,000}$.
answered Jan 15 at 23:15
fleabloodfleablood
70.1k22685
$endgroup$
Don't confuse yourself.
Use simpler terms. "three quarters of an inch" means "$3times frac 14$ inch" or "$frac 3{4}$ inch".
It does not mean "one three$times$fourth" = "$frac 1{3times 4}=frac 1{12}$ inch"
Like wise "three ten-millionths of an inch" means "$3 times frac 1{10,000,000} = frac 3{10,000,000}$"
It does not mean $frac 1{3times 10,000,000} = frac {1 }{30,000,000}$.
answered Jan 15 at 23:15
fleabloodfleablood
70.1k22685
answered Jan 15 at 23:15
fleabloodfleablood
70.1k22685
answered Jan 15 at 23:15
fleabloodfleablood
70.1k22685
answered Jan 15 at 23:15
fleabloodfleablood
70.1k22685
70.1k22685
$begingroup$
Now that actually explains it in extremely simple terms, thank you!
$endgroup$
– PerpetualJ
Jan 15 at 23:17
add a comment |
$begingroup$
Now that actually explains it in extremely simple terms, thank you!
$endgroup$
– PerpetualJ
Jan 15 at 23:17
$begingroup$
Now that actually explains it in extremely simple terms, thank you!
$endgroup$
– PerpetualJ
Jan 15 at 23:17
$begingroup$
Now that actually explains it in extremely simple terms, thank you!
$endgroup$
– PerpetualJ
Jan 15 at 23:17
add a comment |
$begingroup$
They are different values, three ten-millionth is $frac{3}{10times 1000000} = 3cdot 10^{-7}$ and thirty-millionth is $frac{1}{30times 1000000}=3.bar{333}cdot 10^{-8}$.
answered Jan 15 at 23:04
Ori KainOri Kain
114
$endgroup$
$begingroup$
That should be three ten-millionths. In the context of this question, the distinction is important! And the OP didn't write thirty-millionth, but thirty-millionths, which is invalid. (But the question has now been edited, I see.)
$endgroup$
– TonyK
Jan 15 at 23:16
add a comment |
$begingroup$
They are different values, three ten-millionth is $frac{3}{10times 1000000} = 3cdot 10^{-7}$ and thirty-millionth is $frac{1}{30times 1000000}=3.bar{333}cdot 10^{-8}$.
answered Jan 15 at 23:04
Ori KainOri Kain
114
$endgroup$
$begingroup$
That should be three ten-millionths. In the context of this question, the distinction is important! And the OP didn't write thirty-millionth, but thirty-millionths, which is invalid. (But the question has now been edited, I see.)
$endgroup$
– TonyK
Jan 15 at 23:16
add a comment |
$begingroup$
They are different values, three ten-millionth is $frac{3}{10times 1000000} = 3cdot 10^{-7}$ and thirty-millionth is $frac{1}{30times 1000000}=3.bar{333}cdot 10^{-8}$.
answered Jan 15 at 23:04
Ori KainOri Kain
114
$endgroup$
They are different values, three ten-millionth is $frac{3}{10times 1000000} = 3cdot 10^{-7}$ and thirty-millionth is $frac{1}{30times 1000000}=3.bar{333}cdot 10^{-8}$.
answered Jan 15 at 23:04
Ori KainOri Kain
114
answered Jan 15 at 23:04
Ori KainOri Kain
114
answered Jan 15 at 23:04
Ori KainOri Kain
114
answered Jan 15 at 23:04
Ori KainOri Kain
114
114
$begingroup$
That should be three ten-millionths. In the context of this question, the distinction is important! And the OP didn't write thirty-millionth, but thirty-millionths, which is invalid. (But the question has now been edited, I see.)
$endgroup$
– TonyK
Jan 15 at 23:16
add a comment |
$begingroup$
That should be three ten-millionths. In the context of this question, the distinction is important! And the OP didn't write thirty-millionth, but thirty-millionths, which is invalid. (But the question has now been edited, I see.)
$endgroup$
– TonyK
Jan 15 at 23:16
$begingroup$
That should be three ten-millionths. In the context of this question, the distinction is important! And the OP didn't write thirty-millionth, but thirty-millionths, which is invalid. (But the question has now been edited, I see.)
$endgroup$
– TonyK
Jan 15 at 23:16
$begingroup$
That should be three ten-millionths. In the context of this question, the distinction is important! And the OP didn't write thirty-millionth, but thirty-millionths, which is invalid. (But the question has now been edited, I see.)
$endgroup$
– TonyK
Jan 15 at 23:16
add a comment |
$begingroup$
Not the same.
Three ten-millionths would be (3/10 million) X 1 inch = 0.3 inches divided by 1 million. Thirty millionths of an inch would be 30 times an inch divided by 1 million. So they are different by two orders of magnitude.
I think 0.3 millionths of an inch would be the right description (not that it is any easier to comprehend...).
I think micro ($10^{-6}$), nano ($10^{-9}$), and pico ($10^{-12}$) come in really handy when dealing with small numbers. For example, 1 millionth of an inch can be called 1 micro-inch or 1 $mu$i. Then, 0.3 millionths of an inch becomes $0.3mu$i or 300 nano-inches.
answered Jan 15 at 23:06
Aditya DuaAditya Dua
1,11418
$endgroup$
$begingroup$
That should be three ten-millionths. And thirty-millionths is not the same as thirty millionths! A thirty-millionth is 1/30 000 000, but thirty millionths is 30/1 000 000.
$endgroup$
– TonyK
Jan 15 at 23:17
$begingroup$
Thanks @TonyK. Edited!
$endgroup$
– Aditya Dua
Jan 15 at 23:43
add a comment |
$begingroup$
Not the same.
Three ten-millionths would be (3/10 million) X 1 inch = 0.3 inches divided by 1 million. Thirty millionths of an inch would be 30 times an inch divided by 1 million. So they are different by two orders of magnitude.
I think 0.3 millionths of an inch would be the right description (not that it is any easier to comprehend...).
I think micro ($10^{-6}$), nano ($10^{-9}$), and pico ($10^{-12}$) come in really handy when dealing with small numbers. For example, 1 millionth of an inch can be called 1 micro-inch or 1 $mu$i. Then, 0.3 millionths of an inch becomes $0.3mu$i or 300 nano-inches.
answered Jan 15 at 23:06
Aditya DuaAditya Dua
1,11418
$endgroup$
$begingroup$
That should be three ten-millionths. And thirty-millionths is not the same as thirty millionths! A thirty-millionth is 1/30 000 000, but thirty millionths is 30/1 000 000.
$endgroup$
– TonyK
Jan 15 at 23:17
$begingroup$
Thanks @TonyK. Edited!
$endgroup$
– Aditya Dua
Jan 15 at 23:43
add a comment |
$begingroup$
Not the same.
Three ten-millionths would be (3/10 million) X 1 inch = 0.3 inches divided by 1 million. Thirty millionths of an inch would be 30 times an inch divided by 1 million. So they are different by two orders of magnitude.
I think 0.3 millionths of an inch would be the right description (not that it is any easier to comprehend...).
I think micro ($10^{-6}$), nano ($10^{-9}$), and pico ($10^{-12}$) come in really handy when dealing with small numbers. For example, 1 millionth of an inch can be called 1 micro-inch or 1 $mu$i. Then, 0.3 millionths of an inch becomes $0.3mu$i or 300 nano-inches.
answered Jan 15 at 23:06
Aditya DuaAditya Dua
1,11418
$endgroup$
Not the same.
Three ten-millionths would be (3/10 million) X 1 inch = 0.3 inches divided by 1 million. Thirty millionths of an inch would be 30 times an inch divided by 1 million. So they are different by two orders of magnitude.
I think 0.3 millionths of an inch would be the right description (not that it is any easier to comprehend...).
I think micro ($10^{-6}$), nano ($10^{-9}$), and pico ($10^{-12}$) come in really handy when dealing with small numbers. For example, 1 millionth of an inch can be called 1 micro-inch or 1 $mu$i. Then, 0.3 millionths of an inch becomes $0.3mu$i or 300 nano-inches.
answered Jan 15 at 23:06
Aditya DuaAditya Dua
1,11418
edited Jan 15 at 23:42
answered Jan 15 at 23:06
Aditya DuaAditya Dua
1,11418
answered Jan 15 at 23:06
Aditya DuaAditya Dua
1,11418
answered Jan 15 at 23:06
Aditya DuaAditya Dua
1,11418
1,11418
$begingroup$
That should be three ten-millionths. And thirty-millionths is not the same as thirty millionths! A thirty-millionth is 1/30 000 000, but thirty millionths is 30/1 000 000.
$endgroup$
– TonyK
Jan 15 at 23:17
$begingroup$
Thanks @TonyK. Edited!
$endgroup$
– Aditya Dua
Jan 15 at 23:43
add a comment |
$begingroup$
That should be three ten-millionths. And thirty-millionths is not the same as thirty millionths! A thirty-millionth is 1/30 000 000, but thirty millionths is 30/1 000 000.
$endgroup$
– TonyK
Jan 15 at 23:17
$begingroup$
Thanks @TonyK. Edited!
$endgroup$
– Aditya Dua
Jan 15 at 23:43
$begingroup$
That should be three ten-millionths. And thirty-millionths is not the same as thirty millionths! A thirty-millionth is 1/30 000 000, but thirty millionths is 30/1 000 000.
$endgroup$
– TonyK
Jan 15 at 23:17
$begingroup$
That should be three ten-millionths. And thirty-millionths is not the same as thirty millionths! A thirty-millionth is 1/30 000 000, but thirty millionths is 30/1 000 000.
$endgroup$
– TonyK
Jan 15 at 23:17
$begingroup$
Thanks @TonyK. Edited!
$endgroup$
– Aditya Dua
Jan 15 at 23:43
$begingroup$
Thanks @TonyK. Edited!
$endgroup$
– Aditya Dua
Jan 15 at 23:43
add a comment |
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2
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It's not clear what you mean by thirty-millionths, because it doesn't make sense as it stands: you might mean thirty millionths (no hyphen!), that is 30/1 000 000; or one thirty-millionth, that is 1/30 000 000. (But neither of these is equal to three ten-millionths, that is 3/10 000 000.)
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– TonyK
Jan 15 at 23:08
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@TonyK Thank you for clarifying that point; I'll edit the post as it was unclear to me what the number was as well; but I would like to believe the first case of $frac{30}{1000000}$. I simply included the hyphen as I didn't understand the nature of its placement there.
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– PerpetualJ
Jan 15 at 23:12
2
$begingroup$
The issue is that the phrase 'a ten-millionth' is a bit misleading, or ambiguous at least, to someone unfamiliar with the terminology. It doesn't mean 'ten millionths'; it means 'a tenth of a millionth'. But you've interpreted it as the former. Just as millionth means 1/(a million), ten-millionth, i.e. (ten-million)th (not ten millionths), means 1/(ten million).
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– AlephNull
Jan 15 at 23:13