Procedure for Ordering Decimals
To compare and order two decimals, follow a four-step procedure that relies on equivalent decimals:
- Write the numbers one under the other, lining up the decimal points. Vertical alignment ensures that digits in the same place value are matched (tenths with tenths, hundredths with hundredths, and so on).
- Equalize the number of decimal places. If one number has fewer digits after the decimal point than the other, append trailing zeros to the shorter number until both have the same number of decimal places. Because trailing zeros do not change a decimal's value, this produces an equivalent decimal.
- Compare the numbers as if they were whole numbers. Ignore the decimal points and compare the digit sequences directly — whichever whole number is larger corresponds to the larger decimal.
- Express the result with the appropriate inequality symbol. Use or to state the ordering of the original decimals.
This method works because once both decimals share the same number of decimal places, they represent fractions with the same power-of-ten denominator, making the comparison as straightforward as comparing two whole numbers.
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