Whole Numbers

Whole numbers describe zero and positive counting quantities through place value, operations, factors, and estimation.

Place value changes by a factor of ten at each step. Adjacent place-value columns are connected by multiply-by-ten and divide-by-ten arrows. A decimal point and scientific-notation form show that notation can change while quantity stays fixed.

Place value gives every digit meaning, and that structure powers every whole-number calculation.

What whole numbers are

The whole numbers are

0,1,2,3,4,\ldots

They include zero and all positive counting numbers, with no fractions, decimals, or negative values. Whole numbers model counts such as books, people, or completed items.

Place value

In base ten, each place is ten times the value of the place to its right. For example,

48\,705=4(10\,000)+8(1000)+7(100)+0(10)+5(1).

The zero is a placeholder showing there are no tens. Removing it would change the number.

Reading, writing, and comparing

Read a number by grouping digits into periods of three: ones, thousands, millions, and so on. Compare whole numbers first by digit count, then from the greatest place value toward the right.

On a number line, the number farther right is greater. Symbols $<$ and $>$ point toward the smaller number.

Addition and subtraction

Align digits by place value. Addition combines quantities; subtraction finds a difference, a missing part, or how much remains.

Inverse operations provide a built-in check.

Common mistakes

Ignoring zeros inside a number. They hold place value.

Aligning digits rather than places. Ones must align with ones.

Treating a remainder the same in every context. Interpret the situation.

Performing addition before multiplication without grouping. Follow operation order.

Accepting an answer without estimating. A quick benchmark catches many errors.

Quick self-check

Can I write the number in expanded place-value form?
Are comparisons based on the first differing place?
Are operations aligned and regrouped by place value?
Can the inverse operation verify the result?
Are factors, multiples, and remainders interpreted correctly?
Is the answer close to a reasonable estimate?