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Decimal Place Value — Definition, Formula & Examples

Decimal place value is the value a digit holds based on its position to the right of the decimal point. Each place is ten times smaller than the one before it: tenths, hundredths, thousandths, and so on.

In the base-ten number system, digits to the right of the decimal point occupy positions whose values are negative powers of ten. The first position represents 10−110^{-1} (one tenth), the second represents 10−210^{-2} (one hundredth), the third represents 10−310^{-3} (one thousandth), and this pattern continues for each successive position.

Key Formula

digit×110n\text{digit} \times \frac{1}{10^{n}}
Where:
  • digit\text{digit} = The digit (0–9) in that decimal position
  • nn = The position number after the decimal point (1 for tenths, 2 for hundredths, 3 for thousandths, etc.)

How It Works

Every digit after the decimal point sits in a named place. The first spot is the tenths place, the second is the hundredths place, and the third is the thousandths place. To find the value a digit contributes, multiply the digit by the value of its place. For example, in 0.47, the 4 is in the tenths place so it represents 4×0.1=0.44 \times 0.1 = 0.4, and the 7 is in the hundredths place so it represents 7×0.01=0.077 \times 0.01 = 0.07. You can add these individual values together to rebuild the original number: 0.4+0.07=0.470.4 + 0.07 = 0.47.

Worked Example

Problem: What is the value of each digit after the decimal point in 3.625?
Step 1: Identify the digit in the tenths place. It is 6.
6×110=0.66 \times \frac{1}{10} = 0.6
Step 2: Identify the digit in the hundredths place. It is 2.
2×1100=0.022 \times \frac{1}{100} = 0.02
Step 3: Identify the digit in the thousandths place. It is 5.
5×11,000=0.0055 \times \frac{1}{1{,}000} = 0.005
Step 4: Add the whole-number part and all the decimal values together.
3+0.6+0.02+0.005=3.6253 + 0.6 + 0.02 + 0.005 = 3.625
Answer: In 3.625, the 6 is worth 0.6 (six tenths), the 2 is worth 0.02 (two hundredths), and the 5 is worth 0.005 (five thousandths).

Another Example

Problem: Which digit is in the hundredths place in 12.908?
Step 1: Move right from the decimal point. The first digit, 9, is in the tenths place.
Step 2: The second digit after the decimal point is 0. That is the hundredths place.
Step 3: Find its value.
0×1100=00 \times \frac{1}{100} = 0
Answer: The digit in the hundredths place is 0, and its value is 0.

Visualization

Why It Matters

Understanding decimal place value is essential in 4th- and 5th-grade math when students begin comparing, rounding, and computing with decimals. It also shows up every day when reading prices, measurements, and sports statistics. In science classes, knowing which decimal place a measurement reaches tells you how precise that measurement is.

Common Mistakes

Mistake: Naming the first place after the decimal point the "oneths" place, mirroring the ones place on the left side.
Correction: There is no "oneths" place. The first position to the right of the decimal point is the tenths place.
Mistake: Thinking that more digits after the decimal point always means a larger number (e.g., believing 0.125 is greater than 0.5).
Correction: Compare digit by digit from left to right. The tenths digit of 0.5 is 5, which is greater than the tenths digit 1 in 0.125, so 0.5 is the larger number.

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