Decimal structure

Powers of ten shift one place at a time

Follow a single nonzero digit from the ones place through the hundred-thousands place.

A nonnegative integer power of ten has the form 10ⁿ. In ordinary positional notation, multiplying by 10 moves the nonzero digit one place to the left: 1, 10, 100, 1,000, 10,000, and 100,000. In the standard Number Atlas family, each value uses a different fixed-value symbol whose meaning does not depend on position.

The rule

Increase the exponent, shift the place

Number-symbol visualization of 10,000 from the reviewed Numerosidad Number Atlas collection. — Curated collection

10,000

Multiply by 10 to move one place left. 6 reviewed decimal powers.
Explore the reviewed page for 10,000

The exponent tells how many factors of 10 are multiplied. For example, 10³ = 10 × 10 × 10 = 1,000.

Multiplying a whole number by 10 shifts every digit one decimal place to the left and introduces a zero in the ones place. For a pure power of ten, one leading 1 is followed by n zeroes.

These six pages cover every supported visual place in the Atlas. One million would require a seventh place and lies outside the current 1 through 999,999 range.

Rule10⁰, 10¹, 10², 10³, 10⁴, 10⁵

Reviewed place shifts

One reviewed page for every supported place

Move in order from one to one hundred thousand and compare which fixed-value symbol represents each power.

Supported decimal places

The exponent and occupied place advance together.

110⁰ = 1; ones 1010¹ = 10; tens 10010² = 100; hundreds 1,00010³ = 1,000; thousands 10,00010⁴ = 10,000; ten-thousands 100,00010⁵ = 100,000; hundred-thousands

Look closely

Patterns worth comparing

One nonzero positional digit

Each numeral has one digit 1 and all other digits 0. Its Atlas image therefore contains one fixed-value symbol of the matching magnitude.

The number of zeroes matches the exponent

10⁴ is 10,000, with four zeroes after the 1. This pattern holds for every nonnegative integer power of ten.

Some powers are squares or cubes

1, 100, and 10,000 are perfect squares; 1 and 1,000 are perfect cubes.

Use the collection

Use powers of ten as a symbol-value key

01
Name the symbol value
Open a page and name the fixed value carried by the single symbol before reading the numeral.
02
Multiply or divide
Move one step in either direction and explain why the value becomes ten times as large or one tenth as large.
03
Use as landmarks
Compare a multi-digit number with the neighboring powers of ten to identify its size and greatest occupied place.

Keep exploring