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Write decimals in expanded notation

Writing a decimal in expanded notation expresses it as the sum of its place-value contributions: for example, 12.305=10+2+0.3+0.00512.305 = 10 + 2 + 0.3 + 0.005, or equivalently 12+310+5100012 + \frac{3}{10} + \frac{5}{1000}. This understanding includes decimals less than or greater than one, zero-valued places, and the fact that each digit’s value depends on its position rather than its face value; the scope is finite decimals through thousandths, excluding scientific notation and repeating decimals.

Detailed Explanation: Write decimals in expanded notation

Expanded notation shows the value of each digit based on its place.

For a decimal:

  • Digits to the left of the decimal point are ones, tens, hundreds, and so on.
  • Digits to the right are tenths, hundredths, and thousandths.
  • A zero contributes 00, so its term can be left out.

Example: Write 204.307204.307 in expanded notation.

  1. Identify the value of each digit:
DigitPlace value2200 (hundreds)00 (tens)44 (ones)30.3 (tenths)00 (hundredths)70.007 (thousandths)\begin{array}{c|c} \text{Digit} & \text{Place value} \\ \hline 2 & 200 \text{ (hundreds)}\\ 0 & 0 \text{ (tens)}\\ 4 & 4 \text{ (ones)}\\ 3 & 0.3 \text{ (tenths)}\\ 0 & 0 \text{ (hundredths)}\\ 7 & 0.007 \text{ (thousandths)} \end{array}
  1. Add the place-value contributions:
204.307=200+0+4+0.3+0+0.007204.307=200+0+4+0.3+0+0.007
  1. Omit the zero terms:
204.307=200+4+0.3+0.007\boxed{204.307=200+4+0.3+0.007}

The digit 77 does not mean 77 whole units. Because it is in the thousandths place, its value is 0.0070.007.

Learn by doing: Write decimals in expanded notation

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    Place Value (Decimals) - Normal Form to Expanded (Numbers)

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