I'm trying to understand a statement I came across: "each digit represents an increasing power of 10." This seems unclear to me because, from my understanding, each digit itself does not represent an increasing power of 10. Instead, the position of each digit in a number corresponds to an increasing power of 10. Am I right?
Source on Youtube Video (1:22 timing): https://youtu.be/Xpk67YzOn5w?si=id-TZM0PZHkWkFgp&t=81
For example, in the number 22706:
digits: ----- |2|2|7|0|6|
positions:- |4|3|2|1|0|
Could someone clarify what is meant by "each digit represents an increasing power of 10"?
The word digit may be used to refer to position in a sequence of values, often together with its place value, so you could for example speak of the ones digit, the tens digit, the hundreds digit and so on. Presumably in a base 2 system you might instead refer to the ones digit, the twos digit, the fours digit and so on. I found this definition and example in a wiktionary link:
digit (mathematics): A position in a sequence of numerals representing a place value in a positional number system.
- Synonyms: place; figure (informal, usually in discussion of money)
- Example Usage: The base-10 number 123.4 has four digits: the hundreds digit is 1, the tens digit is 2, the units digit is 3, and the tenths digit is 4.
Of course digit also has its other and probably more common meaning, which is a symbol used to represent the numbers in a positional number system, such as the digits 0,1,...9 in the base 10 system or the digits 0,1,...F in the base 16 system.