# Naming the procedure of converting the place values of digits

Let's say I have the numeral 2.263,3 thousands, and convert it to 2.263.300 units.

How do we describe what I have done to the numeral regarding units ?

I know it has to do with the place values of the positions of digits

• You have multiplied it by a thousand. You have converted the units. Sep 20 at 10:40
• @ryang Different cultures use different symbols for the decimal separator and the thousands separator. 1,000.5 (i.e. one thousand and a half) in the US is written as 1.000,5 in other cultures (Belgium being one of them) Sep 26 at 6:19
• @ryang Well now you know. Sep 26 at 6:33
• @ryang "those who use commas as a decimal marker use periods as a thousands separator" if "those" means "all of those" then that's incorrect. If "those" means "some of those" then it's true. Some cultures also just use a space for thousands separators.
– Stef
Sep 26 at 14:38
• @ryang also note some cultures group digits by 4 rather than by 3 (ie powers of 10000 are considered more natural than powers of 1000)
– Stef
Sep 26 at 16:46

I think this is just called "converting between place value."

If you Google that phrase, you'll see tons of hits that include problems like the one you referenced.

For instance, IXL (one of the most popular sites for practicing math problems) has a problem type called "convert between place value" in its 4th grade math contents: https://www.ixl.com/math/grade-4/convert-between-place-values

I don't believe there is a set phrase for this, other than "conversion". However, conversion is very broad because it also includes factors that are not powers of the base that you are working in.

When the conversion factor is not a power of the base you're working in (e.g. multiplying a base 10 number by any number that is not a power of 10), the number's digits will change instead of only shifting the decimal separator left or right.
Imperial units are a classic example of this, and this added complexity is generally why proponents of the metric system claim it to be superior to the imperial system.

If you specifically want to focus on moving the decimal separator without otherwise altering the digits, and you're not sufficiently happy with "moving the decimal separator", I would suggest the neologisms digit shift (for any base) or decimal shift (specifically for base 10).

The suggestion of "digit shift" is based on the established name for bit shifting, which specifically refers to doing this in binary, where the digits are named "bits". In all other bases, there is no particular nickname for the digits (ternary's "trits" are more often than not used jokingly rather than genuinely), so "digit shift" seems the better choice here.

The suggestion of "decimal shift" is based on "bit shift" also being known as "binary shift" (see linked wiki page where it says: "Binary shift" redirects here). Binary is base 2, decimal is base 10, so "decimal shift" would be an analogous name for the same operation in base 10.

It is called converting of units: if you have 2.263,3 m you can convert it to 226.330cm o 2263.3300mm and so on . when you write 2.263,3 thousands probably you mean in units 2.263,3*1m=2.263,3m *1000mm/m

When the "thousands" are given as SI prefix "k", then it's just transforming the "k" to the corresponding power of 10:

$$2.263,3 \text { k[unit]} = 2.263,3 \cdot 10^3 \text{[unit]} = 2.263.300 \text{[unit]}$$