Editing Numerical digit (section)

===Computation of place values===
The [[decimal]] numeral system uses a [[decimal separator]], commonly a [[period (punctuation)|period]] in English, or a [[comma]] in other [[Europe]]an languages,<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Decimal Point|url=https://mathworld.wolfram.com/DecimalPoint.html|access-date=2020-07-22|website=mathworld.wolfram.com|language=en}}</ref> to denote the "ones place" or "units place",<ref>{{Cite book|author=Snyder, Barbara Bode|title=Practical math for the technician : the basics|date=1991|publisher=Prentice Hall|isbn=0-13-251513-X|location=Englewood Cliffs, N.J.|pages=225|oclc=22345295|quote=units or ones place}}</ref><ref name="Rickoff1888">{{cite book|author=Andrew Jackson Rickoff|title=Numbers Applied|url=https://books.google.com/books?id=IYvSWIw3oxUC&pg=PA5|year=1888|publisher=D. Appleton & Company|pages=5–|quote=units' or ones' place}}</ref><ref name="McClymondsJones1905">{{cite book|author1=John William McClymonds|author2=D. R. Jones|title=Elementary Arithmetic|url=https://books.google.com/books?id=xwYAAAAAYAAJ&pg=PA17|year=1905|publisher=R.L. Telfer|pages=17–18|quote=units' or ones' place}}</ref> which has a place value one. Each successive place to the left of this has a place value equal to the place value of the previous digit times the [[radix|base]]. Similarly, each successive place to the right of the separator has a place value equal to the place value of the previous digit divided by the base. For example, in the numeral '''10.34''' (written in [[base&nbsp;10]]),
:the '''0''' is immediately to the left of the separator, so it is in the ones or units place, and is called the ''units digit'' or ''ones digit'';<ref name="JohnsonLendsey1967">{{cite book|author1=Richard E. Johnson|url=https://books.google.com/books?id=W4AXAQAAMAAJ|title=Introductory Algebra for College Students|author2=Lona Lee Lendsey|author3=William E. Slesnick|publisher=Addison-Wesley Publishing Company|year=1967|page=30|quote=units' or ones', digit}}</ref><ref name="PierceTebeaux1983">{{cite book|author1=R. C. Pierce|author2=W. J. Tebeaux|title=Operational Mathematics for Business|url=https://books.google.com/books?id=ng11FOHjNmcC|year=1983|publisher=Wadsworth Publishing Company|isbn=978-0-534-01235-9|page=29|quote=ones or units digit}}</ref><ref name="Sobel1985a">{{cite book|author=Max A. Sobel|title=Harper & Row algebra one|url=https://books.google.com/books?id=f3Y51BtCOKMC|year=1985|publisher=Harper & Row|isbn=978-0-06-544000-3|page=282|quote=ones, or units, digit}}</ref>
:the '''1''' to the left of the ones place is in the tens place, and is called the ''tens digit'';<ref name="Sobel1985b">{{cite book|author=Max A. Sobel|title=Harper & Row algebra one|url=https://books.google.com/books?id=f3Y51BtCOKMC|year=1985|publisher=Harper & Row|isbn=978-0-06-544000-3|page=277|quote=every two-digit number can be expressed as 10t+u when t is the tens digit}}</ref>
:the '''3''' is to the right of the ones place, so it is in the tenths place, and is called the ''tenths digit'';<ref name=":0">{{Cite book|author=Taggart, Robert|title=Mathematics. Decimals and percents|date=2000|publisher=J. Weston Walch|isbn=0-8251-4178-8|location=Portland, Me.|pages=51–54|oclc=47352965}}</ref>
:the '''4''' to the right of the tenths place is in the hundredths place, and is called the ''hundredths digit''.<ref name=":0" />

The total value of the number is 1 ten, 0 ones, 3 tenths, and 4 hundredths. The zero, which contributes no value to the number, indicates that the 1 is in the tens place rather than the ones place.

The place value of any given digit in a numeral can be given by a simple calculation, which in itself is a complement to the logic behind numeral systems. The calculation involves the multiplication of the given digit by the base raised by the exponent {{nowrap|''n'' − 1}}, where ''n'' represents the position of the digit from the separator; the value of ''n'' is positive (+), but this is only if the digit is to the left of the separator. And to the right, the digit is multiplied by the base raised by a negative (−) ''n''. For example, in the number '''10.34''' (written in base&nbsp;10),
:the '''1''' is second to the left of the separator, so based on calculation, its value is,

:<math>n - 1 = 2 - 1 = 1</math>

:<math>1 \times 10^1 = 10</math>

:the '''4''' is second to the right of the separator, so based on calculation its value is,

:<math>n = -2</math>

:<math>4 \times 10^{-2} = \frac{4}{100}</math>