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Place Value & Base-10 Explorer

Type any number to see its place value chart, base-10 blocks, expanded form, and word form. Supports whole numbers up to millions and decimals down to hundredths. All computation runs in your browser.

Supports whole numbers up to 9,999,999 and decimals to hundredths

Try an example

Standard Form

3,456

Expanded Form

3,000+400+50+63,000 + 400 + 50 + 6

Word Form

three thousand four hundred fifty-six

Place Value Chart

thousandshundredstensones
3456
1,000100101

Base-10 Blocks

Flat (100)Rod (10)Cube (1)

Reference Guide

The Place Value System

Our number system is base-10. Each place is 10 times the value of the place to its right.

…  1000  ∣  100  ∣  10  ∣  1  .  110  ∣  1100\ldots \; 1000 \; | \; 100 \; | \; 10 \; | \; 1 \; . \; \tfrac{1}{10} \; | \; \tfrac{1}{100}

The digit 5 in the hundreds place means 500, but in the tens place it means 50. Position determines value.

Expanded Form

Expanded form writes a number as the sum of each digit times its place value.

3,456=3,000+400+50+63{,}456 = 3{,}000 + 400 + 50 + 6

This is useful for understanding what each digit contributes to the total value and for practicing addition with regrouping.

Base-10 Blocks

Base-10 blocks are physical or visual representations of place value.

  • Unit cube = 1
  • Rod = 10 (a row of 10 cubes)
  • Flat = 100 (a 10 × 10 square)
  • Cube = 1,000 (a 10 × 10 × 10 block)

Ten of one block always equals one of the next larger block.

Decimal Place Values

The decimal point separates whole-number places from fractional places. To the right of the decimal, each place is one-tenth of the previous.

42.75=40+2+0.7+0.0542.75 = 40 + 2 + 0.7 + 0.05

The 7 is in the tenths place (worth 0.7) and the 5 is in the hundredths place (worth 0.05).