Core decimal rule
Align decimal points. Add placeholder zeros. Compare digits from left to right.
Example: 3.405 becomes 3.405, while 3.45 becomes 3.450.
Negative decimal rule
Any negative number is below zero. Among negatives, greater magnitude means a smaller value.
Example: −2.4 < −0.75 because −2.4 lies farther left.
Percentage conversion
Divide the percentage by one hundred before comparing.
Formula: decimal = percentage ÷ 100.
Fraction conversion
Divide the numerator by the denominator before ordering.
Formula: decimal = numerator ÷ denominator.
- Enter decimals, integers, fractions, percentages, or scientific notation.
- Select an ordering direction and a duplicate-handling method.
- Choose raw comparison, rounding, banker’s rounding, or truncation.
- Enable the explanations, statistics, place values, and number line you need.
- Press “Order these values” to calculate and display the complete result.
- Use export controls to download CSV, JSON, PDF, or number-line files.
Why decimal alignment matters
Decimal comparison becomes reliable when every decimal point is aligned. Placeholder zeros make unequal lengths easier to inspect. The zeros do not change a number’s value.
Consider 4.5 and 4.05. Writing 4.50 beside 4.05 exposes the first unequal decimal place. Five tenths exceed zero tenths.
Working with negative decimals
Negative values reverse common magnitude intuition. A number farther from zero on the negative side is smaller. Therefore, negative 8.2 is below negative 3.9.
The number line provides a useful visual check. Values increase while moving from left to right. Zero separates negative and positive values.
Equivalent decimal forms
Decimal forms may look different while representing equal values. For example, 0.5, 0.50, one-half, and 50 percent are equal. Group mode reveals these equivalences.
Preserving the original entry remains useful for teaching. Numeric comparison can use converted values while reports retain entered formats. This calculator displays both forms.
Precision changes and ordering
Rounding can change equality and order. Values that differ slightly may become identical at a selected precision. The calculator warns when processing changes inputs.
Raw comparison is best for exact entered values. Standard rounding is familiar for everyday work. Banker’s rounding can reduce repeated rounding bias.
Using statistics after sorting
Sorting supports more than visual comparison. It helps identify the median, quartiles, range, percentiles, and repeated modes. Consecutive differences show spacing between values.
These measures are optional and separate from ordering. They can support classroom exercises, data checking, and quick exploratory analysis. Exported reports preserve the key results.