Decimal Place Value Formula

Decimal place value is the value assigned to each digit's position to the right of the decimal point: the first position is tenths (1/10), the second is.

The Formula

0.46=4 tenths+6 hundredths0.46=4\text{ tenths}+6\text{ hundredths}

When to use: Just as moving left of the decimal point makes each place 10 times bigger (ones, tens, hundreds), moving right makes each place 10 times smaller (tenths, hundredths, thousandths). It's like zooming in—each step splits things into 10 equal pieces.

Quick Example

3.847:3=ones,  8=tenths(810),  4=hundredths(4100),  7=thousandths(71000)3.847: \quad 3 = \text{ones}, \; 8 = \text{tenths} \left(\frac{8}{10}\right), \; 4 = \text{hundredths} \left(\frac{4}{100}\right), \; 7 = \text{thousandths} \left(\frac{7}{1000}\right)

Notation

Each place to the right of the decimal is one tenth of the place before it.

What This Formula Means

The value assigned to each digit's position to the right of the decimal point: the first position is tenths (110\frac{1}{10}), the second is hundredths (1100\frac{1}{100}), the third is thousandths (11000\frac{1}{1000}), and so on.

Just as moving left of the decimal point makes each place 10 times bigger (ones, tens, hundreds), moving right makes each place 10 times smaller (tenths, hundredths, thousandths). It's like zooming in—each step splits things into 10 equal pieces.

Formal View

For a decimal d0.d1d2d3…:  value=d0×100+d1×10−1+d2×10−2+d3×10−3+⋯=∑k=0ndk×10−k\text{For a decimal } d_0.d_1 d_2 d_3 \ldots: \; \text{value} = d_0 \times 10^0 + d_1 \times 10^{-1} + d_2 \times 10^{-2} + d_3 \times 10^{-3} + \cdots = \sum_{k=0}^{n} d_k \times 10^{-k}

Worked Examples

Example 1

easy
In the number 4.73, identify the value of each digit.

Answer

4 ones, 7 tenths, 3 hundredths

First step

1
4 is in the ones place: value = 4.

Full solution

  1. 2
    7 is in the tenths place: value = 710=0.7\frac{7}{10} = 0.7.
  2. 3
    3 is in the hundredths place: value = 3100=0.03\frac{3}{100} = 0.03.
  3. 4
    Total: 4+0.7+0.03=4.734 + 0.7 + 0.03 = 4.73.
Place value tells us what a digit is worth. Moving right of the decimal point: tenths (÷10), hundredths (÷100), thousandths (÷1000), etc.

Example 2

medium
Write 3 hundredths, 5 tenths, and 2 ones as a single decimal number.

Example 3

medium
In the number 45.037245.0372, what is the place value of the digit 3?

Common Mistakes

  • Saying the 6 in 0.460.46 is six tenths — it is six hundredths.
  • Lining up decimal operations by the right edge — line up decimal points so places match.
  • Thinking 0.50.5 is smaller than 0.460.46 because it has fewer digits — compare tenths first.

Why This Formula Matters

Most decimal mistakes are place-value mistakes. If students can name tenths, hundredths, and thousandths, they can compare decimals, align operations, and convert to fractions accurately. Recognizing it by "Can I name the place of the digit I am using?" — rather than by familiar numbers — is what lets a student tell it apart from decimals and rounding in a mixed problem set.

Frequently Asked Questions

What is the Decimal Place Value formula?

The value assigned to each digit's position to the right of the decimal point: the first position is tenths (110\frac{1}{10}), the second is hundredths (1100\frac{1}{100}), the third is thousandths (11000\frac{1}{1000}), and so on.

How do you use the Decimal Place Value formula?

Just as moving left of the decimal point makes each place 10 times bigger (ones, tens, hundreds), moving right makes each place 10 times smaller (tenths, hundredths, thousandths). It's like zooming in—each step splits things into 10 equal pieces.

What do the symbols mean in the Decimal Place Value formula?

Each place to the right of the decimal is one tenth of the place before it.

Why is the Decimal Place Value formula important in Math?

Most decimal mistakes are place-value mistakes. If students can name tenths, hundredths, and thousandths, they can compare decimals, align operations, and convert to fractions accurately. Recognizing it by "Can I name the place of the digit I am using?" — rather than by familiar numbers — is what lets a student tell it apart from decimals and rounding in a mixed problem set.

What do students get wrong about Decimal Place Value?

The procedure for decimal place value is the easy part; the trap is saying the 6 in 0.460.46 is six tenths. Asking "Can I name the place of the digit I am using?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

What should I learn before the Decimal Place Value formula?

Before studying the Decimal Place Value formula, you should understand: place value.

Want the Full Guide?

This formula is covered in depth in our complete guide:

Place Value and Measurement: Number Sense Foundations →
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