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Place value

Explain what each digit contributes to a number. Read zeros as placeholders and use place value to compare, split, and rebuild whole numbers.

Fraction pieces and simple shapes illustrate relationships between numbers.

What you’ll learn

  • Read a digit’s value from its position.
  • Write a number as a sum of place-value parts.
  • Compare multi-digit numbers from the highest differing place.

Position changes a digit’s value

In base ten, each whole-number place is worth ten times the place immediately to its right. The digit 4 represents forty in 40 and four thousand in 4,000.

Zero keeps a place open

In 4,305, the zero shows that there are no tens. Decomposing the number as 4,000 + 300 + 5 preserves that position even though the zero contributes no amount.

A mistake to avoid

Do not compare two numbers by looking at their largest individual digit. Compare corresponding places from the left after checking how many places each number has.

Worked example

Compare 5,081 and 5,108

Both numbers have 5 thousands. Their hundreds differ: 0 hundreds is less than 1 hundred. Therefore 5,081 < 5,108; the 8 in the first number does not make it larger.

Learning paths that include this skill

Choose the route that fits your goal. The same skill can be useful in more than one subject or stage of learning.