Decimal Place Values

The place value system does not stop at the ones column. To the right of the decimal point, positions continue with values that are fractions of one. These are the decimal place values: tenths, hundredths, thousandths, and beyond.

Decimal place value has its roots in the Hindu-Arabic numeral system, developed in India by around the 5th to 7th century CE, where mathematicians were among the first to treat zero as a true number and to use position, rather than separate symbols, to show whether a digit meant ones, tens, or hundreds. That system reached Europe through the 9th-century work of the Persian scholar Muhammad ibn Musa al-Khwarizmi and, later, Fibonacci's 1202 book Liber Abaci. Extending place value to the right of the decimal point came later still: the Flemish mathematician Simon Stevin formally introduced decimal fractions in his 1585 book De Thiende (“The Art of Tenths”), showing for the first time how tenths, hundredths, and thousandths could be written and calculated using the same place-value logic as whole numbers.

Decimal place value is at work anywhere a measurement needs more precision than a whole number allows. Currency is written in decimal form almost everywhere in the world (like $4.99 or €12.50), scientific measurements are recorded to as many decimal places as the instrument allows, and sports timing, fuel gauges, and weather forecasts all rely on tenths, hundredths, or thousandths of a unit. Getting comfortable with decimal place value is what makes it possible to read, compare, and calculate with all of these everyday numbers correctly.

The Decimal Point

A decimal point separates the whole number part (to its left) from the fractional part (to its right).

Decimal Place Value Chart

Reading a Decimal Number

Every digit's value depends entirely on where it sits. The same digit can be worth a hundred times more or a hundred times less depending on its position, which is exactly why place value matters so much: to read a decimal number correctly, first read the whole part as an ordinary number, then say "and" or "point", then read the decimal digits as a single group and name the place of the final digit — not each digit's place individually.

Here is why the position matters so much: in the number 4.372, the digit 3 sits in the tenths place, so it is worth 3/10 = 0.3. Move that same digit 3 one place further right and it becomes worth only 3/100 = 0.03 — ten times smaller, even though the digit itself hasn't changed.

Practice: Identify the Digit's Value

A digit in the number below is highlighted. If you get its value wrong (or leave it blank), we'll walk through exactly how to work it out.

Expanded Form for Decimals

Expanded form breaks a number down into the sum of the values of each of its digits, which is another way of showing exactly how place value builds up the whole number. Every non-zero digit contributes one term to the sum; digits that are 0 contribute nothing, so they are simply left out of the expanded form.

Here is a fuller example showing every step, including a placeholder zero that gets skipped:

Practice: Build the Decimal from Its Parts

The expanded form of a decimal number is shown below. If you get the combined number wrong (or leave it blank), we'll add the parts together with you, one step at a time.

Linking Decimals and Fractions

Comparing Decimals – Common Mistake

More decimal digits does not mean a larger number.

Summary

Decimal place values mirror whole-number place values but extend to the right of the decimal point. Each position represents a fraction whose denominator is a power of 10. Mastering decimal place values is essential for working with money, measurements, percentages and scientific data.