NumberExpand

The place-value terms of $n$: each digit times its power of the base.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageNumberExpand✓↗

NumberExpand(n)the base-10 place-value terms of $n$

NumberExpand(n, base)place-value terms in the given base

NumberExpand(n, base, len)padded to len digits (leading zero terms) first

Typed signatures

Type	Package	Applies
(integer, integer?, integer?) -> list	numerals	always

Domain: Numeral systems

Details

• The terms sum back to $n$: Total(NumberExpand(n)) is $n$
• Every term carries the sign of $n$, not just the leading one

Examples

Basic #

live ↗

In$\mathrm{NumberExpand}(1\,234)$Out$\bigl\lbrack1\,000, 200, 30, 4\bigr\rbrack$

Splits into place-value parts $100+50+7$

live ↗

In$\mathrm{NumberExpand}(157)$Out$\bigl\lbrack100, 50, 7\bigr\rbrack$

Base 2 expansion keeps zero places: $128+16+8+4+1$

live ↗

In$\mathrm{NumberExpand}(157, 2)$Out$\bigl\lbrack128, 0, 0, 16, 8, 4, 0, 1\bigr\rbrack$

live ↗

In$\mathrm{NumberExpand}(157, 2, 3)$Out$\bigl\lbrack128, 0, 29\bigr\rbrack$

Scope #

base 2, zero terms kept

live ↗

In$\mathrm{NumberExpand}(10, 2)$Out$\bigl\lbrack8, 0, 2, 0\bigr\rbrack$

every term carries the sign

live ↗

In$\mathrm{NumberExpand}(-123)$Out$\bigl\lbrack-100, -20, -3\bigr\rbrack$

Each digit scaled by its power of ten

live ↗

In$\mathrm{NumberExpand}(1\,437)$Out$\bigl\lbrack1\,000, 400, 30, 7\bigr\rbrack$

Negative numbers give negative parts

live ↗

In$\mathrm{NumberExpand}(-14\,379)$Out$\bigl\lbrack-10\,000, -4\,000, -300, -70, -9\bigr\rbrack$

Properties #

Each term is a digit times a place value

live ↗

In$\mathrm{NumberExpand}(1\,532)$Out$\bigl\lbrack1\,000, 500, 30, 2\bigr\rbrack$

Base 10 is the default

live ↗

In$\mathrm{NumberExpand}(1\,532, 10)$Out$\bigl\lbrack1\,000, 500, 30, 2\bigr\rbrack$

live ↗

In$\mathrm{NumberExpand}(1\,437, 10, 8)$Out$\bigl\lbrack1\,000, 400, 30, 7, 0, 0, 0, 0\bigr\rbrack$

About

Examples	11
Checked against	Wolfram Language 11 agree
Crosswalk	Wolfram Language

See also: IntegerDigits, IntegerLength