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Decimals and Place Value

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.

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.

Larger Place Value:

Arrow shows direction of greater place value.

472

Unit position number (1 x)

Tens position number

(10 x unit position)

Hundreds position number

(100 x unit position)

472.

or

Smaller Place Value:

Arrow showing direction place value is decreasing.

.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.

17,472,593

Ten million position

(10,000,000 times unit position)

Larger

Larger place value arrow.

Smaller

Smaller place value arrow.

Ten millionths position

(4/10,000,000)

.28675844