Choose the concentration basis before entering values. Then label the denominator as the final solution, normalize compatible units, and retain the basis in the answer.
Three supplied records, three different outputs
OpenStax defines mass percentage using component mass divided by solution mass, volume percentage using component volume divided by solution volume, and mass-volume concentration using a mass relative to solution volume. The m/v convention used here reports grams per 100mL. OpenStax concentration units.
Use these original fictional composition records as a paper arithmetic exercise. They are separate supplied records, not observations of one material or instructions for preparing a mixture.
| Record | Selected basis | Component quantity | Final solution quantity | Expected answer |
|---|---|---|---|---|
| C1 | Mass/mass | 5g | 125g | 4% m/m |
| C2 | Volume/volume | 5mL | 125mL | 4% v/v |
| C3 | Mass/volume | 5g | 125mL | 4g per 100mL, labeled 4% m/v |
For C1, calculate (5g / 125g) × 100 = 4. The mass units cancel, and the answer retains the m/m label. For C2, the matching volume units cancel instead. For C3, the quantities do not form a dimensionless mass fraction: (5g / 125mL) × 100mL = 4g.
The companion displays the three basis labels and the corresponding output units. “4%” alone erases the distinction the reader came to resolve.
Use final solution quantity, not solvent alone
C1's primary denominator is the supplied final solution mass of 125g. A separate optional closed accounting record gives component mass 5g and solvent mass 120g, totaling 125g. That supports the same denominator for this record.
Using (5 / 120) × 100 would give about 4.17 parts of component per 100 parts of solvent; it does not produce C1's mass percentage. Keep “final solution mass” on the input label so that the wrong denominator is harder to enter accidentally.
Do not extend that addition example to guess C2's final volume from separate component volumes. C2 already supplies the final solution volume. The packet also supplies no density linking any mass to any volume, so it cannot convert C1 into C2 or C3. Same numeral, different record, different basis.
Normalize units within the chosen basis
An alternate entry for C1 is component mass 5000mg and final solution mass 0.125kg. Normalize both to grams: 5000mg is 5g and 0.125kg is 125g. The result remains 4% m/m.
Record both the entered quantities and their normalized forms in the worksheet key. Dividing the raw numerals 5000 and 0.125 skips the unit conversion and gives a meaningless result for this task.
For C3, normalize compatible mass units to grams and compatible volume units to milliliters before applying the declared grams-per-100mL convention. Converting milligrams to grams is a unit change within a quantity type. Guessing grams from milliliters requires information this packet does not contain.
Distinguish zero from missing and inconsistent inputs
Use an explicit validation ledger for the companion:
| Input condition | Expected treatment |
|---|---|
| Component zero, final solution positive | Valid arithmetic result zero, with the selected basis |
| Blank component or denominator | Incomplete; no result |
| Negative or nonfinite value | Invalid input; no result |
| Final solution quantity zero | Invalid denominator; no result |
| C1-type component mass above final solution mass | Inconsistent composition record |
| Volume-mode component above final volume | Outside this helper's declared fictional-record scope |
The volume-mode restriction is a bounded input contract for this exercise, not a claim that component volumes always add. Do not carry the mass-mode 100% ceiling into m/v: grams per 100mL is a mixed-unit concentration, not a dimensionless portion of total mass.
If the reader changes basis, clear the old quantities, units, answer, and active feedback. If an input changes within one basis, invalidate the previous answer until a new calculation is completed. An answer left beside revised inputs can look correct while belonging to an earlier record.
Use the helper as a labeled reading aid
The native worksheet and checked key should remain the evidence for the exercise. The HTML companion lets a reader select C1, C2, or C3, inspect the matching fields, calculate, and clear the record. Check the same cases after changing the companion.
In this use, the value is seeing the denominator, normalized quantities, and output label together. The worksheet remains the source; rendering an answer does not establish an actual composition measurement.
Copyable worksheet-and-helper prompt
Create one complete, self-contained US-English HTML companion for “Concentration · Choose the Basis”. Return the full HTML document, with inline CSS and any JavaScript needed for the local interactions. Use the original scenario, named records, numbers and expected cases below.
Design the page for this task: use clearly labeled input or source records, a readable result or worked example, and an adjacent explanation of the evidence. Use a restrained visual hierarchy, left-aligned text, readable tables or stacked records, and a responsive layout at 720px and 360px. Provide meaningful labeled controls for Mass / mass Output: % m/m; Volume / volume Output: % v/v; Mass / volume Output: g per 100 mL; Calculate; Load supplied record; Clear. Use keyboard-accessible native controls and visible focus. Keep the complete content readable without an external dependency.
The following brief supplies the substantive content and constraints. Native-format requests describe the material to represent or copy manually; this HTML must not pretend to create DOCX, XLSX, PDF, PPTX, H5P or another native file, run Python/Flask/Django/Snowflake/Power BI, connect a live service, send messages, or perform an authorized real-world action. Where the task requires a native source, actual observation or separate approval, retain that requirement and leave unsupplied evidence blank.
Prepare an English percentage-concentration worksheet, checked expected-results key, and specification for an original basis-labeled HTML helper. Do not claim runtime checks that you have not performed. Use supplied fictional records only; provide no preparation recipe or actual measurement claim.
C1: mass/mass, component 5g, final solution 125g, answer 4% m/m. C2: volume/volume, component 5mL, final solution 125mL, answer 4% v/v. C3: mass/volume, component 5g, final solution 125mL, answer 4g per 100mL, also labeled 4% m/v. These are separate records, not interchangeable descriptions of one material.
Show selected basis, entered quantities, normalized quantities, final-solution denominator, calculation, and fully labeled answer together. C1's optional closed accounting record contains 5g component and 120g solvent, totaling 125g. Do not divide by 120g. Alternate C1 entries 5000mg and 0.125kg normalize to 5g and 125g and retain 4% m/m. Do not guess density, convert across bases, or derive final volume by adding component volumes.
Allow zero component with a positive final quantity. Hold blank, negative, nonfinite, and zero-denominator cases without an answer. Mass-mode component above total mass is inconsistent. Restrict volume-mode fixtures to component no greater than final volume as a local scope rule, not universal volume additivity. Do not impose a universal 100 ceiling on the mixed-unit m/v answer.
Changing basis clears old quantities, units, result and active feedback. Editing inputs invalidates the old result until recalculated. Specify useful Calculate and Clear behavior and keyboard/focus states, with actual runtime and narrow-screen tests pending. Retain the native worksheet/key as authoritative.
COMPLETE AUTHORED SCENARIO AND EXPECTED CASES
The following is the supplied reading/teaching/calculation record to represent in the companion. Preserve its particular content, examples, source references and unknowns. Wording about a future native implementation refers to that native task, not permission to omit this HTML companion.
# Percentage Concentration Calculator: Choose the Basis First
Your worksheet says “5 in 125,” and a calculator returns 4%. That answer is incomplete until you know what the two quantities measure. Five grams in 125 grams, five milliliters in 125 milliliters, and five grams in 125 milliliters produce the same numeral with different meanings.
Choose the concentration basis before entering values. Then label the denominator as the final solution, normalize compatible units, and retain the basis in the answer.
## Three supplied records, three different outputs
OpenStax defines mass percentage using component mass divided by solution mass, volume percentage using component volume divided by solution volume, and mass-volume concentration using a mass relative to solution volume. The m/v convention used here reports grams per 100mL. [OpenStax concentration units](https://openstax.org/books/chemistry-2e/pages/3-4-other-units-for-solution-concentrations).
Use these original fictional composition records as a paper arithmetic exercise. They are separate supplied records, not observations of one material or instructions for preparing a mixture.
| Record | Selected basis | Component quantity | Final solution quantity | Expected answer |
| --- | --- | --- | --- | --- |
| C1 | Mass/mass | 5g | 125g | 4% m/m |
| C2 | Volume/volume | 5mL | 125mL | 4% v/v |
| C3 | Mass/volume | 5g | 125mL | 4g per 100mL, labeled 4% m/v |
For C1, calculate `(5g / 125g) × 100 = 4`. The mass units cancel, and the answer retains the m/m label. For C2, the matching volume units cancel instead. For C3, the quantities do not form a dimensionless mass fraction: `(5g / 125mL) × 100mL = 4g`.
The companion displays the three basis labels and the corresponding output units. “4%” alone erases the distinction the reader came to resolve.
## Use final solution quantity, not solvent alone
C1's primary denominator is the supplied final solution mass of 125g. A separate optional closed accounting record gives component mass 5g and solvent mass 120g, totaling 125g. That supports the same denominator for this record.
Using `(5 / 120) × 100` would give about 4.17 parts of component per 100 parts of solvent; it does not produce C1's mass percentage. Keep “final solution mass” on the input label so that the wrong denominator is harder to enter accidentally.
Do not extend that addition example to guess C2's final volume from separate component volumes. C2 already supplies the final solution volume. The packet also supplies no density linking any mass to any volume, so it cannot convert C1 into C2 or C3. Same numeral, different record, different basis.
## Normalize units within the chosen basis
An alternate entry for C1 is component mass 5000mg and final solution mass 0.125kg. Normalize both to grams: 5000mg is 5g and 0.125kg is 125g. The result remains 4% m/m.
Record both the entered quantities and their normalized forms in the worksheet key. Dividing the raw numerals 5000 and 0.125 skips the unit conversion and gives a meaningless result for this task.
For C3, normalize compatible mass units to grams and compatible volume units to milliliters before applying the declared grams-per-100mL convention. Converting milligrams to grams is a unit change within a quantity type. Guessing grams from milliliters requires information this packet does not contain.
## Distinguish zero from missing and inconsistent inputs
Use an explicit validation ledger for the companion:
| Input condition | Expected treatment |
| --- | --- |
| Component zero, final solution positive | Valid arithmetic result zero, with the selected basis |
| Blank component or denominator | Incomplete; no result |
| Negative or nonfinite value | Invalid input; no result |
| Final solution quantity zero | Invalid denominator; no result |
| C1-type component mass above final solution mass | Inconsistent composition record |
| Volume-mode component above final volume | Outside this helper's declared fictional-record scope |
The volume-mode restriction is a bounded input contract for this exercise, not a claim that component volumes always add. Do not carry the mass-mode 100% ceiling into m/v: grams per 100mL is a mixed-unit concentration, not a dimensionless portion of total mass.
If the reader changes basis, clear the old quantities, units, answer, and active feedback. If an input changes within one basis, invalidate the previous answer until a new calculation is completed. An answer left beside revised inputs can look correct while belonging to an earlier record.
## Use the helper as a labeled reading aid
The native worksheet and checked key should remain the evidence for the exercise. The HTML companion lets a reader select C1, C2, or C3, inspect the matching fields, calculate, and clear the record. Check the same cases after changing the companion.
In this use, the value is seeing the denominator, normalized quantities, and output label together. Keep the required native records authoritative; rendering an answer does not establish an actual composition measurement. [Explore NOS](https://nos-workspace.com/).
Implement the local companion rather than returning a text-only plan. Preserve every numerical fixture and the distinction between illustrative expectations and actual evidence. Any native-runtime or classroom tests mentioned above remain tests to perform in the proper environment; do not mark them passed. Keep edits and practice responses in this open page only, without claiming persistent storage. Provide invalid/missing-input feedback and reset behavior that agree with this specific brief. Do not claim accessibility certification, learning gains, real approvals or test results that were not observed.
Before you accept the numeral, finish the sentence: four percent by which basis, and divided by what final solution quantity?