Measurement Uncertainty Flashcards: Absolute & Percentage Practice
Practice 42 measurement uncertainty prompts: absolute and percentage amounts, arithmetic handoffs, and mistake repairs under a stated classroom interval model.
Про цю колоду
An uncertainty amount needs a meaning before it can enter arithmetic. These 42 measurement uncertainty flashcards practice a stated classroom linear interval model with original short calculations, operation choices, mixed-step handoffs, and mistake repairs.
Here, x ± Δx specifies permitted values from x − Δx to x + Δx. All combinations of distinct input values are allowed. This is an exercise model, not a probability distribution or evidence about actual apparatus. Addition, subtraction, and exact scaling use exact interval widths. Products, quotients, and powers use explicitly labeled first-order estimates from summed relative contributions; those estimates are not generally exact symmetric bounds. Positive nominal inputs and denominator intervals above zero keep these tasks within that limited scope.
You'll retrieve an interval from a nominal value and half-width; convert absolute amounts to percentages and selected percentages back to absolute amounts; choose the right representation for an operation; and carry a calculated difference into a later quotient or a product into a later sum. A few repairs target adding percentages before a sum, subtracting contributions in a quotient, failing to scale a width, and reading uncertainty from decimal digits. Exact product and quotient endpoints make the approximation boundary visible. A few conceptual cards distinguish standard uncertainties from interval half-widths and identify the need to check covariance assumptions. They do not teach a second computation syllabus.
The sequence introduces interval meaning and representations before dependent calculations, then interleaves conversions, arithmetic, handoffs, repairs, and model limits. Same-concept variants have at least three unrelated cards between them. Long-term spacing belongs to the review scheduler.
You should already be comfortable with percentages and ordinary arithmetic. This is an evergreen topic deck, not a complete physics course or an exam-aligned package. It excludes instrument-resolution estimates, half-range rules, correlation and reused-input calculations, logarithms, trigonometric propagation, zero nominal values, denominators that reach zero, full professional uncertainty budgets, and clinical or safety decisions. Mechanical reversals of worked results are omitted because the inputs are generally not determined by an answer. The one reporting task states its rounding convention explicitly.
The numerical setups, prompts, explanations, and sequence were independently authored and checked by interval endpoints, exact fraction or decimal arithmetic, and first-order mathematical expansions. The distinction between uncertainty models was checked against BIPM's uncertainty definition, NIST's basic definitions, and NIST's combination rules. AQA's mathematical requirements establish that these arithmetic operations are familiar learner tasks; this deck does not claim curriculum alignment.
AI tools assisted with drafting, sequencing, and the decorative cover. Every final front and back was manually read during author review; numerical answers also have an exact-arithmetic audit. The cover was inspected at full size and across intended small crops. No apparatus experiment, learner trial, or professional credential is claimed. The original wording, organization, metadata, and generated cover are shared under CC0 1.0 to the extent applicable rights exist. The underlying facts remain common knowledge; cited material retains its own rights.
This is independent, unofficial study practice, with no affiliation to or endorsement by BIPM, NIST, or AQA. No examination questions, mark schemes, curriculum text, source exercises, competitor cards, logos, or trade dress were copied or adapted. See the linked official AQA requirements for its own course scope.
Картки в цій колоді
Картка 1
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. A length is 6.40 ± 0.08 cm. What interval does this specify?
Відповідь
6.32 to 6.48 cm.
Subtract and add the supplied half-width: 6.40 − 0.08 and 6.40 + 0.08.
Картка 2
Питання
In the classroom interval model, how do you turn an absolute half-width Δx into a percentage for a positive nominal value x?
Відповідь
100 × Δx / x percent.
Use the same unit for Δx and x. The ratio Δx/x is the relative amount before multiplying by 100.
Картка 3
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. For a difference a − b, which expression gives its exact absolute half-width?
Відповідь
Δa + Δb.
The largest difference pairs the upper value of a with the lower value of b; the smallest pairs the opposite endpoints.
Картка 4
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. A quantity is multiplied by an exact positive factor k. What happens to its absolute half-width?
Відповідь
Multiply it by k.
Both endpoints scale by k.
Картка 5
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. Use first-order summed relative contributions. For z = ab with positive a and b and small relative half-widths, what relative amount do you use for z?
Відповідь
Δa/a + Δb/b, approximately.
Multiplying the nominal product by this sum gives its first-order absolute amount. The omitted product ΔaΔb prevents this from being a general exact symmetric bound.
Картка 6
Питання
A measurement is printed as 17.2 s, with no uncertainty statement. Can its uncertainty be determined from those digits alone?
Відповідь
No.
The displayed digits do not specify an interval, a standard deviation, or a coverage probability. An uncertainty statement and its meaning are needed.
Картка 7
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. Add 9.60 ± 0.06 mm and 3.40 ± 0.02 mm. What is the total’s exact absolute half-width?
Відповідь
0.08 mm.
Add the widths: 0.06 + 0.02. The nominal total is 13.00 mm.
Картка 8
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. A nominal mass of 72 g has a 1.5% interval half-width. What is its absolute half-width?
Відповідь
1.08 g.
72 × 1.5/100 = 1.08. This converts the supplied percentage; it does not estimate an instrument’s uncertainty.
Картка 9
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. A positive quantity has a 1.2% half-width. For its fourth power, what is the first-order percentage amount?
Відповідь
Approximately 4.8%.
Multiply 1.2% by the magnitude of the exact exponent: 4 × 1.2%. This is a linear estimate, not an exact power interval.
Картка 10
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. A model length 9.60 ± 0.24 mm is divided by exactly 12. What is the result’s exact absolute half-width?
Відповідь
0.020 mm.
0.24/12 = 0.020. The nominal result is 0.80 mm; the exact divisor adds no uncertainty contribution.
Картка 11
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. Subtract 12.10 ± 0.02 cm from 18.70 ± 0.03 cm. What is the difference’s exact absolute half-width?
Відповідь
0.05 cm.
0.03 + 0.02 = 0.05. The nominal difference is 6.60 cm; subtracting nominal values does not subtract the interval widths.
Картка 12
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. Use first-order summed relative contributions. Multiply lengths 4.00 ± 0.04 cm and 9.00 ± 0.18 cm. What is the product’s approximate percentage amount?
Відповідь
Approximately 3.0%.
The contributions are 0.04/4.00 = 1.0% and 0.18/9.00 = 2.0%. Add them for the first-order product estimate.
Картка 13
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. Use first-order summed relative contributions. Divide 84.0 ± 0.42 m by 7.00 ± 0.14 s. What is the quotient’s approximate absolute amount?
Відповідь
Approximately 0.30 m/s.
The nominal quotient is 12 m/s. Its relative amount is 0.42/84.0 + 0.14/7.00 = 0.025, so 12 × 0.025 = 0.30 m/s.
Картка 14
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. A calculated force is 42.0 ± 0.21 N. What is its percentage half-width?
Відповідь
0.50%.
100 × 0.21/42.0 = 0.50. Use the calculated quantity’s own nominal value in the denominator.
Картка 15
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. A positive length has a 0.75% half-width. What is the first-order percentage amount for its square?
Відповідь
Approximately 1.50%.
The exact exponent is 2, so multiply the relative amount by 2. Do not square the percentage.
Картка 16
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. A permitted length interval runs from 9.90 to 10.10 cm. What is its absolute half-width?
Відповідь
0.10 cm.
Half the interval’s full width is (10.10 − 9.90)/2 = 0.10 cm. Its midpoint is 10.00 cm.
Картка 17
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. Convert 0.875 ± 0.003 m to centimeters using the exact factor 100 cm per meter. What is the absolute half-width in centimeters?
Відповідь
0.30 cm.
100 × 0.003 m = 0.30 cm. Convert the width along with the nominal value, which becomes 87.5 cm.
Картка 18
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. Two time values are 22.40 ± 0.08 s and 16.40 ± 0.04 s. What percentage half-width belongs to their positive difference before a later ratio?
Відповідь
2.0%.
The difference is 6.00 s with half-width 0.08 + 0.04 = 0.12 s. Then 100 × 0.12/6.00 = 2.0%.
Картка 19
Питання
A student says that writing 7.80 g establishes an interval half-width of 0.01 g. Is that conclusion supported by the notation alone?
Відповідь
No.
The final decimal place is not an uncertainty model. Ask for the supplied uncertainty and whether it is a bound, a standard uncertainty, or another stated quantity.
Картка 20
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. Use first-order summed relative contributions. A calculated sum is S = 36.0 ± 0.18 cm. Multiply it by a distinct length 8.00 ± 0.04 cm. What is the area’s approximate absolute amount?
Відповідь
Approximately 2.88 cm².
The nominal area is 288 cm². The relative contributions are 0.18/36.0 = 0.005 and 0.04/8.00 = 0.005, so 288 × 0.010 = 2.88 cm².
Картка 21
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. Use first-order summed relative contributions. For a quotient of positive quantities, the numerator’s contribution is 2% and the denominator’s is 3%. A student subtracts them. What approximate percentage should replace that step?
Відповідь
Approximately 5%.
The linear interval estimate adds the magnitudes of the relative contributions for a quotient: 2% + 3%.
Картка 22
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. A is 80.0 ± 0.4 cm and B is 30.0 ± 0.3 cm. Which has the larger percentage half-width?
Відповідь
B.
A has 100 × 0.4/80.0 = 0.5%; B has 100 × 0.3/30.0 = 1.0%. A larger absolute amount need not be larger in percentage terms.
Картка 23
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. A positive quantity has a 1.6% half-width. What is the first-order percentage amount for its square root?
Відповідь
Approximately 0.8%.
The exact exponent is 1/2. Multiply 1.6% by 1/2; do not take the square root of the percentage.
Картка 24
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. Add masses 7.80 ± 0.03 g and 4.20 ± 0.05 g, then divide by exactly 4. What is the final exact absolute half-width?
Відповідь
0.020 g.
Add the widths first, then scale: (0.03 + 0.05)/4 = 0.020 g. The nominal final value is 3.00 g.
Картка 25
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. A rectangle has sides 2.00 ± 0.02 cm and 3.00 ± 0.03 cm. What is its exact permitted area interval?
Відповідь
5.8806 to 6.1206 cm².
Both sides stay positive. Multiply the lower endpoints for the minimum: 1.98 × 2.97. Multiply the upper endpoints for the maximum: 2.02 × 3.03.
Картка 26
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. A length 7.00 ± 0.07 m is multiplied by exactly 5. A student keeps 0.07 m as the result’s half-width. What should replace it?
Відповідь
0.35 m.
The exact factor scales both nominal value and half-width: 5 × 0.07 = 0.35 m. The nominal result is 35.00 m.
Картка 27
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. Use first-order summed relative contributions. Evaluate q = (a − b)/t using a = 46.0 ± 0.12 cm, b = 34.0 ± 0.06 cm, and t = 3.00 ± 0.03 s. What is q’s approximate percentage amount?
Відповідь
Approximately 2.5%.
The difference is 12.0 cm with half-width 0.18 cm, giving 1.5%. Add the time’s 1.0% contribution for the later quotient.
Картка 28
Питання
A worksheet supplies ± amounts but never says whether they are interval half-widths or standard uncertainties. Can you choose addition of widths or root-sum-square from that notation alone?
Відповідь
No.
First identify what the amounts mean and how the inputs relate. Root-sum-square combines suitable standard-uncertainty contributions under its stated assumptions; it does not turn interval half-widths into standard deviations.
Картка 29
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. Use first-order summed relative contributions. Two positive factors have percentage contributions of 1% and 4%. A student multiplies the percentages. What approximate percentage belongs to the product?
Відповідь
Approximately 5%.
Add the first-order relative contributions: 1% + 4%. Multiplying percentages does not give the linear interval estimate.
Картка 30
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. A rectangle has sides 2.00 ± 0.02 cm and 3.00 ± 0.03 cm. Its first-order area estimate is 6.00 ± 0.12 cm². Does that symmetric interval contain every permitted area?
Відповідь
No.
The exact upper endpoint is 2.02 × 3.03 = 6.1206 cm², beyond 6.12 cm². The omitted cross term is 0.02 × 0.03 = 0.0006 cm².
Картка 31
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. A positive quantity x has a 1.0% half-width. For x raised to the exact power −3, what is the first-order percentage amount?
Відповідь
Approximately 3.0%.
Use the magnitude of the exponent: 3 × 1.0% = 3.0%. The reciprocal power does not create a negative uncertainty.
Картка 32
Питання
In a classroom linear interval calculation, a computed force has nominal value 60 N and a first-order percentage amount of 2.4%. What approximate absolute amount corresponds to it?
Відповідь
Approximately 1.44 N.
60 × 2.4/100 = 1.44 N. Convert the final quantity’s percentage using its own nominal value.
Картка 33
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. Add 40.0 ± 0.4 g and 60.0 ± 0.3 g. A student adds the input percentages and reports 1.5%. What percentage half-width should the sum have?
Відповідь
0.70%.
The sum is 100.0 g with absolute half-width 0.4 + 0.3 = 0.7 g. Convert after adding: 100 × 0.7/100.0 = 0.70%.
Картка 34
Питання
Before using a classroom first-order quotient estimate with denominator y ± Δy and positive y, what inequality keeps its entire denominator interval above zero?
Відповідь
y > Δy.
The lower endpoint y − Δy must be positive. A finite quotient interval cannot be assumed when the denominator interval reaches zero.
Картка 35
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. A length 8.00 ± 0.08 m is divided by exactly 100. What is the result’s percentage half-width?
Відповідь
1.0%.
The result is 0.0800 ± 0.0008 m. Both quantities scale together, so 100 × 0.0008/0.0800 remains 1.0%.
Картка 36
Питання
In NIST’s standard-uncertainty model, what does a standard uncertainty represent?
Відповідь
An estimated standard deviation.
It is a different input quantity from a permitted-interval half-width. The same ± notation does not make the two interchangeable.
Картка 37
Питання
A classroom interval model specifies 11.0 ± 0.2 cm as permitted values, with no probability distribution. Does this justify a 95% coverage claim?
Відповідь
No.
A permitted interval in this exercise model does not assign probabilities. A coverage claim needs a justified probabilistic interpretation.
Картка 38
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. Use first-order summed relative contributions. Form ab + c with a = 6.00 ± 0.06 cm, b = 5.00 ± 0.05 cm, and distinct c = 20.00 ± 0.10 cm². What is the final first-order absolute amount?
Відповідь
Approximately 0.70 cm².
The product’s nominal value is 30 cm² and its relative amount is 1% + 1% = 2%, giving 0.60 cm². For the later addition, add absolute amounts: 0.60 + 0.10 = 0.70 cm².
Картка 39
Питання
A classroom first-order interval calculation carries nominal value 13.846 cm and approximate absolute amount 0.274 cm. Report the amount to two significant figures and the nominal value to the same decimal place. What report follows?
Відповідь
Approximately (13.85 ± 0.27) cm.
0.274 rounds to 0.27 cm; its last place is hundredths. Round 13.846 to that place. This uses the supplied reporting convention, not a universal rule.
Картка 40
Питання
For combined standard uncertainty, can the covariance terms always be dropped just because there are two input measurements?
Відповідь
No.
Uncorrelated input estimates justify dropping the covariance contributions. Otherwise their effect must be checked; a count of inputs does not establish the relationship.
Картка 41
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. For positive quantities a = 6.00 ± 0.06 and b = 2.00 ± 0.02, what is the exact interval for a/b? Give exact fractions.
Відповідь
297/101 to 101/33.
The minimum is 5.94/2.02 = 297/101; the maximum is 6.06/1.98 = 101/33. They are about 2.940594 and 3.060606, so the deviations from the nominal 3 are asymmetric.
Картка 42
Питання
Classroom linear interval model; all combinations of distinct input values are allowed. Subtract 98.0 ± 0.10 m from 100.0 ± 0.10 m. What is the difference’s exact percentage half-width?
Відповідь
10%.
The nominal difference is 2.0 m and its half-width is 0.20 m. Thus 100 × 0.20/2.0 = 10%; a small difference can have a large relative amount.
42 картки
Measurement Uncertainty Flashcards: Absolute & Percentage Practice
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