Convert terminating decimals exactly or choose a nearest denominator. Compare inch fractions, rounding differences, metric values, and practical limits.
Quick answer
To convert a decimal to fraction form, write the decimal over a power of ten and reduce, or choose a denominator and round the numerator for a practical approximation. For example, 0.375 = 375/1000 = 3/8 exactly. A nearest-denominator result is approximate unless converting it back produces the original decimal value.
Standard (Woodworking) • 0" - 1"
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Precision: 1/64" • Range 0" - 1"
| Decimal (in) | Fraction | Metric (mm) |
|---|---|---|
| 0.0000 | 0" | 0.000 |
| 0.0156 | 1/64" | 0.397 |
| 0.0313 | 1/32" | 0.794 |
| 0.0469 | 3/64" | 1.191 |
| 0.0625 | 1/16" | 1.587 |
| 0.0781 | 5/64" | 1.984 |
| 0.0938 | 3/32" | 2.381 |
| 0.1094 | 7/64" | 2.778 |
| 0.1250 | 1/8" | 3.175 |
| 0.1406 | 9/64" | 3.572 |
| 0.1563 | 5/32" | 3.969 |
| 0.1719 | 11/64" | 4.366 |
| 0.1875 | 3/16" | 4.762 |
| 0.2031 | 13/64" | 5.159 |
| 0.2188 | 7/32" | 5.556 |
| 0.2344 | 15/64" | 5.953 |
| 0.2500 | 1/4" | 6.350 |
| 0.2656 | 17/64" | 6.747 |
| 0.2813 | 9/32" | 7.144 |
| 0.2969 | 19/64" | 7.541 |
| 0.3125 | 5/16" | 7.938 |
| 0.3281 | 21/64" | 8.334 |
| 0.3438 | 11/32" | 8.731 |
| 0.3594 | 23/64" | 9.128 |
| 0.3750 | 3/8" | 9.525 |
| 0.3906 | 25/64" | 9.922 |
| 0.4063 | 13/32" | 10.319 |
| 0.4219 | 27/64" | 10.716 |
| 0.4375 | 7/16" | 11.112 |
| 0.4531 | 29/64" | 11.509 |
| 0.4688 | 15/32" | 11.906 |
| 0.4844 | 31/64" | 12.303 |
| 0.5000 | 1/2" | 12.700 |
| 0.5156 | 33/64" | 13.097 |
| 0.5313 | 17/32" | 13.494 |
| 0.5469 | 35/64" | 13.891 |
| 0.5625 | 9/16" | 14.287 |
| 0.5781 | 37/64" | 14.684 |
| 0.5938 | 19/32" | 15.081 |
| 0.6094 | 39/64" | 15.478 |
| 0.6250 | 5/8" | 15.875 |
| 0.6406 | 41/64" | 16.272 |
| 0.6563 | 21/32" | 16.669 |
| 0.6719 | 43/64" | 17.066 |
| 0.6875 | 11/16" | 17.462 |
| 0.7031 | 45/64" | 17.859 |
| 0.7188 | 23/32" | 18.256 |
| 0.7344 | 47/64" | 18.653 |
| 0.7500 | 3/4" | 19.050 |
| 0.7656 | 49/64" | 19.447 |
| 0.7813 | 25/32" | 19.844 |
| 0.7969 | 51/64" | 20.241 |
| 0.8125 | 13/16" | 20.637 |
| 0.8281 | 53/64" | 21.034 |
| 0.8438 | 27/32" | 21.431 |
| 0.8594 | 55/64" | 21.828 |
| 0.8750 | 7/8" | 22.225 |
| 0.8906 | 57/64" | 22.622 |
| 0.9063 | 29/32" | 23.019 |
| 0.9219 | 59/64" | 23.416 |
| 0.9375 | 15/16" | 23.813 |
| 0.9531 | 61/64" | 24.209 |
| 0.9688 | 31/32" | 24.606 |
| 0.9844 | 63/64" | 25.003 |
| 1.0000 | 1" | 25.400 |
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Start with the exact rows most often needed for eighth-inch marks and ordinary arithmetic. This decimal to fraction reference uses 0.125 = 1/8, .25 = 1/4, .375 = 3/8, .5 = 1/2, .625 = 5/8, .75 = 3/4, and .875 = 7/8. A leading zero is recommended in technical records, so write 0.25 rather than .25 when clarity matters. These decimal to fraction values remain mathematically exact because each terminating decimal can be written over a power of ten and reduced without changing its value. For example, 0.625 becomes 625/1000, then 5/8 after both terms are divided by 125.
A decimal to fraction chart is especially fast when the decimal already lands on a familiar denominator. It does not make every nearby decimal equal to that row. The decimal 0.62 is 31/50 exactly, not 5/8; 5/8 is 0.625. If a task limits the available marks to eighths, 5/8 may be the nearest usable mark, but it must be identified as an approximation. For any decimal to fraction result, preserve the original value, state the chosen denominator, and distinguish an equality from a rounded choice. That small record prevents a convenient chart row from silently replacing the source measurement. Use the decimal to fraction table as a representation aid, not as evidence that a measurement, part, recipe, or drawing is correct.
This decimal to fraction check starts with the unrounded source value.
| Decimal | Fraction | Millimeters |
|---|---|---|
| 0.1250 | 1/8 | 3.175 |
| 0.2500 | 1/4 | 6.350 |
| 0.3750 | 3/8 | 9.525 |
| 0.5000 | 1/2 | 12.700 |
| 0.6250 | 5/8 | 15.875 |
| 0.7500 | 3/4 | 19.050 |
| 0.8750 | 7/8 | 22.225 |
The exact decimal to fraction method for a terminating decimal has three steps. First, count the digits to the right of the decimal point. Second, remove the point and place the resulting integer over 10, 100, 1000, or the corresponding power of ten. Third, divide numerator and denominator by their greatest common divisor. Thus 0.375 becomes 375/1000. The greatest common divisor is 125, so the reduced answer is 3/8. For 2.125, separate the whole number or use an improper fraction: 2.125 = 2125/1000 = 17/8 = 2 1/8.
Keep the sign when the input is negative. For example, -0.75 becomes -75/100 and reduces to -3/4. Trailing zeros do not alter the mathematical value: 0.5000 and 0.5 both reduce to 1/2. However, trailing zeros may communicate measurement resolution in a laboratory, drawing, or production record, so do not remove them from the source record merely because the decimal to fraction answer reduces cleanly.
This decimal to fraction power-of-ten process gives an exact result for every finite decimal. It may produce a denominator that is not convenient on a ruler or gauge. In that situation, exact conversion and practical nearest-denominator conversion are different tasks. Complete the exact decimal to fraction calculation first if mathematical equivalence matters. Only then choose whether a rounded shop or layout fraction is useful, and label that second output as nearest or approximate.
A decimal to fraction equality must survive back-conversion.
A nearest-denominator decimal to fraction conversion restricts the answer to fractions whose denominator divides a selected scale, such as 8, 16, 32, or 64. Let x be the decimal and d the selected denominator. Calculate n = round(x × d), form n/d, and reduce it by the greatest common divisor. The represented decimal is n ÷ d. The absolute rounding difference is |x − n/d|. Report that difference with the original units whenever the distinction can affect the task.
For 0.343 at a denominator of 32, calculate round(0.343 × 32) = round(10.976) = 11. The nearest result is 11/32, whose decimal value is 0.34375. The absolute difference is 0.00075. Therefore, 0.343 ≈ 11/32; it is not correct to print an equals sign between them. By contrast, the decimal to fraction calculation for 0.375 at denominator 32 gives 12/32, which reduces to 3/8 and converts back to 0.375 exactly.
In decimal to fraction rounding, a smaller interval can reduce the possible rounding difference, but it does not improve the original measurement. The denominator is a display or mark-selection choice, not a tolerance. If an input falls exactly halfway between two allowed fractions, apply the tool’s stated tie rule consistently and record it. Do not assume every calculator resolves ties the same way. A reproducible decimal to fraction workflow stores the input, units, denominator, tie rule, rounded fraction, represented decimal, and signed or absolute difference.
Record the denominator used for each decimal to fraction approximation.
The most important reading rule is simple: an exact decimal to fraction result converts back to the original value with no difference. A nearest result is approximate when the converted fraction differs from the input. Use “=” only for equality and “≈” or the words “nearest fraction” for approximation. This distinction matters even when a screen rounds both values to the same number of displayed digits. Hidden digits can still carry a difference that affects later calculations.
Consider 0.2. Its exact fraction is 1/5 because 1 ÷ 5 is exactly 0.2. If the available ruler marks are sixteenths, the nearest allowed value is 3/16, or 0.1875, rather than 1/5. The exact decimal to fraction answer and the nearest ruler mark are both useful, but they answer different questions. Likewise, 0.1 inch is exactly 1/10 inch; calling it 3/32 inch changes the represented value.
In decimal to fraction work, do not infer acceptance from a small-looking difference. A permissible difference comes from the controlling drawing, recipe objective, inspection plan, process sheet, product specification, or other task requirement. The chart has none of that context. Preserve significant source digits and units, especially when values move between software or people. When a decimal to fraction approximation is copied into a note, include the original decimal nearby. When the fraction is later converted back, use the stored fraction rather than a rounded display string. These practices keep exact arithmetic separate from task-specific judgment and make the decimal to fraction trail reviewable.
That decimal to fraction distinction keeps equality separate from convenience.
Identify the unit before using any decimal to fraction chart. A decimal value written in feet must first be interpreted as feet; it is not automatically a decimal number of inches. For example, 0.5 foot equals 6 inches, while 0.5 inch equals 1/2 inch. The same digits describe lengths that differ by a factor of twelve. Similarly, 0.25 foot equals 3 inches, whereas 0.25 inch equals 1/4 inch.
Construction dimensions sometimes combine whole feet with decimal feet. In 8.25 feet, the 0.25-foot part is 3 inches, so the combined length is 8 feet 3 inches. It is not 8 feet 1/4 inch. Multiply the fractional-foot portion by 12 to obtain decimal inches, then perform the decimal to fraction step on the inch remainder if a fractional-inch form is needed. Thus 6.375 feet contains 0.375 × 12 = 4.5 inches and can be written as 6 feet 4 1/2 inches. Keep the original unit in the record because stripping it away creates ambiguity.
Surveying, architectural, estimating, and calculator outputs can use different formats, including decimal feet, feet-and-decimal-inches, or feet-inches-fractions. Confirm the format from the source rather than guessing from punctuation. A decimal to fraction answer cannot repair an incorrect unit assumption. Before transferring a dimension to a tape measure, label each stage: source feet, converted decimal inches, and final fractional inches. This unit-first decimal to fraction practice prevents a numerically tidy but physically wrong result.
Unit labels come before any decimal to fraction step.
| Decimal Value | As Feet | As Inches |
|---|---|---|
| 0.1 | 1.2" | 1/10" |
| 0.25 | 3" | 1/4" |
| 0.5 | 6" | 1/2" |
| 0.75 | 9" | 3/4" |
Kitchen decimals often describe a portion of a cup, tablespoon, teaspoon, ounce, or batch. Apply decimal to fraction arithmetic only after identifying the unit. For a US cup, 0.25 cup is 1/4 cup, 0.5 cup is 1/2 cup, and 0.75 cup is 3/4 cup. Because one US cup contains 16 US tablespoons, 0.125 cup is 1/8 cup or 2 tablespoons, and 0.625 cup is 5/8 cup or 10 tablespoons. These relationships depend on using the same named volume system throughout.
Recipe entries such as 0.33 or 0.67 are usually rounded displays, not exact versions of 1/3 or 2/3. One third is 0.333… and two thirds is 0.666…. Treating 0.33 as exactly 1/3 changes the value. For ordinary cooking the practical difference may be unimportant, but the recipe’s scale, ingredient behavior, and measuring tools determine that—not the decimal to fraction chart. Baking formulas by weight should remain by weight unless a reliable ingredient-specific conversion is available; volume and mass are not interchangeable without density information.
For decimal to fraction work in a scaled recipe, calculate from the original quantity before rounding to a utensil mark. If the computed amount is 0.4375 cup, the exact decimal to fraction result is 7/16 cup, but that mark may not appear on a measuring cup. Converting it to 7 tablespoons is often easier because 0.4375 × 16 = 7. Record substitutions or practical rounding when repeatability matters. This keeps the decimal to fraction conversion transparent while recognizing that kitchen tools and ingredients introduce context beyond arithmetic.
Keep recipe context beside the decimal to fraction result.
A repeating decimal to fraction conversion is exact only when the repeating pattern is known. The notation 0.333… means the threes continue indefinitely and equals 1/3. A typed value of 0.333 without an ellipsis or repeat bar is the finite fraction 333/1000, not 1/3. Likewise, 0.666… = 2/3, 0.1666… with only the 6 repeating = 1/6, 0.111… = 1/9, 0.222… = 2/9, and 0.8333… with only the 3 repeating = 5/6.
Algebra gives a reliable method. Let x = 0.333…. Then 10x = 3.333…. Subtract x from 10x to obtain 9x = 3, so x = 3/9 = 1/3. For a two-digit repeat such as x = 0.272727…, multiply by 100: 100x = 27.272727…. Subtract to get 99x = 27, then reduce 27/99 to 3/11. When nonrepeating digits come before the cycle, align the repeating tails with appropriate powers of ten before subtracting.
Do not add an imagined repeating pattern to a measured or rounded display. A calculator reading of 0.333 may be a rounded presentation of an unknown underlying value. Keep the source precision and notation. A decimal to fraction tool that accepts repeating input should expose which digits repeat; otherwise its finite input is handled as a terminating decimal or nearest-denominator approximation. This notation discipline makes each decimal to fraction statement mathematically testable.
Repeating notation makes the decimal to fraction claim testable.
| Decimal | Fraction | Notation |
|---|---|---|
| 0.333… | 1/3 | 0.3̅ |
| 0.666… | 2/3 | 0.6̅ |
| 0.166… | 1/6 | 0.16̅ |
| 0.111… | 1/9 | 0.1̅ |
| 0.222… | 2/9 | 0.2̅ |
| 0.833… | 5/6 | 0.83̅ |
In woodworking and layout, decimal to fraction output can map a decimal plan dimension to visible tape-measure marks. Choose the denominator supported by the actual scale, compare the represented decimal with the source, and mark the result as nearest when it differs. For drill-bit comparison, a nearby fraction identifies a candidate size only. Check the bit’s actual designation, measured diameter, hole requirement, material, process, and clearance before use. A matching-looking row does not establish fit.
For CNC work, retain the controlling decimal or model value in the machine workflow unless approved documentation explicitly calls for a fractional substitute. Decimal to fraction conversion is useful for communication, manual setup references, and inspection orientation, but it does not validate offsets, tool condition, machine capability, workholding, thermal effects, material response, or the finished feature. Verify the program, setup sheet, current drawing revision, units, datum scheme, inspection method, and authorized tolerance source under the organization’s process. Do not derive a tolerance from the selected denominator or the number of digits shown.
Aerospace work requires the same boundary with stricter procedural attention: a web decimal to fraction chart does not approve a part, accept an inspection result, or authorize a drawing change. Use controlled engineering data, approved planning, calibrated equipment as required by the governing quality system, independent checks where the procedure requires them, and qualified signoff. Record any conversion and its rounding difference so reviewers can reproduce it. For CNC or aerospace decisions, the controlling document and approved verification process outrank every decimal to fraction convenience value.
Controlled requirements outrank a decimal to fraction lookup.
The international inch is defined as exactly 25.4 millimeters. Convert inches to millimeters by multiplying by 25.4, and convert millimeters to inches by dividing by 25.4. This exact unit relationship does not make a rounded input or display exact. For example, 1/8 inch × 25.4 equals 3.175 millimeters exactly as a unit conversion. If a screen displays 3.18 millimeters, that display is rounded. Keep 3.175 or the original 1/8 inch when later calculation needs the exact converted value.
Metric input adds a stage before nearest fractional-inch selection. For 10 millimeters, divide by 25.4 to obtain approximately 0.3937008 inch. A denominator-limited decimal to fraction step may then return a nearby fractional inch, but that fraction is an approximation to 10 millimeters unless its exact metric equivalent is 10 millimeters. Show both conversion stages and avoid presenting the final fraction as though it were the original metric specification.
During decimal to fraction work, round only after the needed calculations, not after every intermediate step. Early rounding can accumulate or change which candidate fraction appears nearest. Store the original value, original unit, converted unrounded working value, denominator, fraction, and difference in one unit. For critical work, confirm unit direction and software settings independently. The exact 25.4 relationship supports traceable arithmetic; it does not certify a measuring instrument or manufacturing process. A sound decimal to fraction workflow keeps definition, measurement quality, display precision, and acceptance criteria separate.
Complete unit conversion before the decimal to fraction selection.
Use the Fraction to Decimal chart when the starting value is fractional, the Decimal to Fraction Inches chart for denominator-based inch work, MM to Inches or Inches to MM for unit conversion, and Drill Bit Sizes for a separate size comparison. Each chart answers a limited question. None selects a tolerance, approves a substitution, or verifies a manufactured feature.
Before leaving the page, review the conversion trail: confirm the source value and unit, decide whether exact equivalence or a nearest denominator is wanted, retain enough digits for the calculation, label approximate output, and consult the controlling requirement for acceptance. That checklist is more important than choosing the largest denominator. The useful outcome of a decimal to fraction conversion is a clear representation whose assumptions can be reconstructed—not an unsupported claim of precision.
Build a complete reference wall with these printable charts.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/64 | 0.0156 | 1.56% |
| 1/32 | 0.0313 | 3.13% |
| 1/16 | 0.0625 | 6.25% |
| 1/8 | 0.1250 | 12.5% |
| 3/16 | 0.1875 | 18.8% |
| 1/4 | 0.2500 | 25% |
| 5/16 | 0.3125 | 31.3% |
| 3/8 | 0.3750 | 37.5% |
| 1/2 | 0.5000 | 50% |
| 3/4 | 0.7500 | 75% |
Fractions from 1/64 to whole numbers for math education and precision cutting.
View chart| Fraction | Decimal | MM |
|---|---|---|
| 1/64" | 0.0156 | 0.40 |
| 1/32" | 0.0313 | 0.79 |
| 1/16" | 0.0625 | 1.59 |
| 1/8" | 0.1250 | 3.18 |
| 3/16" | 0.1875 | 4.76 |
| 1/4" | 0.2500 | 6.35 |
| 5/16" | 0.3125 | 7.94 |
| 3/8" | 0.3750 | 9.53 |
| 1/2" | 0.5000 | 12.70 |
| 5/8" | 0.6250 | 15.88 |
Convert inch fractions to decimals for woodworking, hardware sizing, and measuring.
View chart| Decimal | Fraction | MM |
|---|---|---|
| 0.0156 | 1/64" | 0.40 |
| 0.0313 | 1/32" | 0.79 |
| 0.0625 | 1/16" | 1.59 |
| 0.1250 | 1/8" | 3.18 |
| 0.1875 | 3/16" | 4.76 |
| 0.2500 | 1/4" | 6.35 |
| 0.3125 | 5/16" | 7.94 |
| 0.3750 | 3/8" | 9.53 |
| 0.5000 | 1/2" | 12.70 |
| 0.6250 | 5/8" | 15.88 |
Convert inch decimals to common fractions for measuring, woodworking, and machining.
View chart| Millimeters | Decimal (in) | Fraction (in) |
|---|---|---|
| 0.5 | 0.020 | 0 |
| 1 | 0.039 | 1/16 |
| 6.35 | 0.250 | 1/4 |
| 12.7 | 0.500 | 1/2 |
| 19 | 0.748 | 3/4 |
| 25.4 | 1.000 | 1 |
| 38.1 | 1.500 | 1 1/2 |
| 50.8 | 2.000 | 2 |
| 76.2 | 3.000 | 3 |
| 101.6 | 4.000 | 4 |
Convert millimeters to inches with decimals and fractions for woodworking and engineering.
View chart