Confused about ciphers in the book 'Arithmetic for the Practical Man'

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I honestly can't summarize it.
I'm reading arithmetic for the practical man (very behind in math) and I'm stuck on finding the amount of ciphers in a number. for context, "In arithmetic, a cipher is an old-fashioned term for the zero digit or any Arabic numeral." The source is Google AI which I know is not the best source but is the only definition I can find that matches to this book.

this is the specific part I can't understand, "a very large number such as 1,000,000,000, which is 1 followed by nine ciphers which is typically written in the form of 10 to the power of 9." my problems are right here he puts the little number but I don't know if it is the power or exponent or something else and then I do not know how to calculate such a number to find how many ciphers there are. the link to where I'm reading this is https://babel.hathitrust.org/cgi/pt?id=mdp.39015053141936&seq=24.

my idea is that the little number is based on how many ciphers would be in the number if you just looked at how many zeros are in an untouched 7-digit number like 1,000,000 instead of 1,356,782 but I doubt this highly. sorry if this is jumbled up, my brain can barely make sense of this.
 
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JOHNTITOR1 said:
TL;DR Summary: I honestly can't summarize it.

I'm reading arithmetic for the practical man (very behind in math) and I'm stuck on finding the amount of ciphers in a number. for context, "In arithmetic, a cipher is an old-fashioned term for the zero digit or any Arabic numeral." The source is Google AI which I know is not the best source but is the only definition I can find that matches to this book.

this is the specific part I can't understand, "a very large number such as 1,000,000,000, which is 1 followed by nine ciphers which is typically written in the form of 10 to the power of 9." my problems are right here he puts the little number but I don't know if it is the power or exponent or something else and then I do not know how to calculate such a number to find how many ciphers there are. the link to where I'm reading this is https://babel.hathitrust.org/cgi/pt?id=mdp.39015053141936&seq=24.

my idea is that the little number is based on how many ciphers would be in the number if you just looked at how many zeros are in an untouched 7-digit number like 1,000,000 instead of 1,356,782 but I doubt this highly. sorry if this is jumbled up, my brain can barely make sense of this.
Okay, so this book is about 100 years old! Cipher is not a term I've come across. Everybody uses digit now.

I would look for a more modern source. There's a lot you can do these days with technology - spreadsheets can be a good, practical way to understand different number formats. In Excel, this would be the scientific format for a number.

In this notation ##10^3 = 1000##, which you say "ten to the three", ##10^6 = 1,000,000##, which is "ten to the six" etc. And ##1.23 \times 10^6 = 1,230,000##, which is "one point two three times ten to the six";or. "one point two three million".

This is a neat shorthand, which is essential for many scientific uses of numbers.
 
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Not only is "cipher" a word that I have never encountered before, on the same page this appears:
1738019324514.png

I have never seen this subscript notation before. I agree that you should find a more modern reference.
 
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JOHNTITOR1 said:
this is the specific part I can't understand, "a very large number such as 1,000,000,000, which is 1 followed by nine ciphers which is typically written in the form of 10 to the power of 9." my problems are right here he puts the little number but I don't know if it is the power or exponent or something else
If I understand correctly, you are asking about the meaning of "##10^9##".

You are correct that the superscripted nine is the "exponent". Or "power". Both words refer to the same thing -- exponentiation. Meanwhile, the ##10## is the "base". ##10^9## means ten to the ninth power. This is the same thing as ##10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10## (the product of nine tens). Or ##1,000,000,000## (with nine zeroes).

In modern science, we normally express very large or very small numbers using scientific notation.

I apologize if this response is not aimed at a proper level.
 
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JOHNTITOR1 said:
TL;DR Summary: I honestly can't summarize it.

I'm reading arithmetic for the practical man (very behind in math) and I'm stuck on finding the amount of ciphers in a number. for context, "In arithmetic, a cipher is an old-fashioned term for the zero digit or any Arabic numeral." The source is Google AI which I know is not the best source but is the only definition I can find that matches to this book.

There are two facts you should consider when reading an old book, which by the way can be very fascinating. Firstly, people haven't had computers. Typesetting was a real time-consuming task. Even with an electric typesetter, it was still cumbersome to change the selection balls. So they used primarily a linear notation with as few extras as possible. That explains sometimes notations we don't use anymore. Secondly, mathematics underwent a transformation in the 50s and 60s driven by Bourbaki. People changed from writing mathematics in prose to writing mathematics in formulas. To put it a bit exaggerated, the transition was from readable texts to a structure like "Definition. Example. Lemma. Proposition. Corollary. Theorem. Exercise." I think one should keep both in mind when comparing old texts with modern texts.
 
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PeroK said:
Okay, so this book is about 100 years old! Cipher is not a term I've come across. Everybody uses digit now.

I would look for a more modern source. There's a lot you can do these days with technology - spreadsheets can be a good, practical way to understand different number formats. In Excel, this would be the scientific format for a number.

In this notation ##10^3 = 1000##, which you say "ten to the three", ##10^6 = 1,000,000##, which is "ten to the six" etc. And ##1.23 \times 10^6 = 1,230,000##, which is "one point two three times ten to the six";or. "one point two three million".

This is a neat shorthand, which is essential for many scientific uses of numbers.
thank you, all this stuff helped a lot, I figured it out.
 
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PeroK said:
Cipher is not a term I've come across.

FactChecker said:
Not only is "cipher" a word that I have never encountered before
I've heard/seen it, but then again, I might be older than either of you. Another context in which the word "cypher" (or "cipher") is used is to describe someone as a complete zero.

However I've never seen the notation used in the attachment ; i.e. ##.0_67##.

To the OP -- yes, get a newer book.
 
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Mark44 said:
Another context in which the word "cypher" (or "cipher") is used is to describe someone as a complete zero.
TIL, LOL. :smile:
 
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A "cypher" is another term for something that is converted from a readable format to something that is not readable. The reader then needs a "key" to convert the coded text into readable format.
 
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Svein said:
A "cypher" is another term for something that is converted from a readable format to something that is not readable. The reader then needs a "key" to convert the coded text into readable format.
Google offers up an explanation how a word that means zero has come to mean a code.
https://www.etymonline.com/word/cipher said:

cipher (n.)​

late 14c., "arithmetical symbol for zero," from Old French cifre "nought, zero," Medieval Latin cifra, which, with Spanish and Italian cifra, ultimately is from Arabic sifr "zero," literally "empty, nothing," from safara "to be empty;" a loan-translation of Sanskrit sunya-s "empty." Klein says Modern French chiffre is from Italian cifra.

The word came to Europe with Arabic numerals. From "zero," it came to mean "any numeral" (early 15c.), then (first in French and Italian) "secret way of writing; coded message" (a sense first attested in English 1520s), because early codes often substituted numbers for letters. Meaning "the key to a cipher or secret writing" is by 1885, short for cipher key (by 1835).

Figurative sense of "something or someone of no value, consequence, or power" is from 1570s.

also from late 14c.
 
  • #13
German uses the word "Ziffer" for the digits 0,1,...,9 which is obviously of the same origin as the word cipher is.
 
  • #14
Jethro Bodine used the word "cipher'n" to describe doing arithmetic.
 
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