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Decimals allow us to write or present numbers that would have a fraction with a denominator of 10 or 10 multiple without the fraction. Place value tells us the mathematical value one digit of a number has to another digit to its left or right.

Larger Place Value:

472

or

472.

Hundreds position number

(100 × unit position)

Tens position number

(10 × unit position)

Unit position number (1 ×)

Moving left each place value position is 10 times greater the position to its right.

Moving right each place value position is 10 times less the position to its left.

Without a decimal a number can never be less than 1 and have value.

Smaller Place Value:

.286

Tenths position (2/10)

Hundredths position (8/100)

Thousandths position (6/1,000)

With place value and decimals, numbers can be as large or small as needed.

Larger

17,472,593

Ten million position

(10,000,000 times unit position)

Smaller

.28675844

Ten millionths position

(4/10,000,000)