Significant Figures Flashcards: Mixed Operations & Rounding
Practice 48 significant figures prompts: report short mixed calculations, track precision handoffs, repair rounding mistakes, and handle explicitly exact inputs.
اس ڈیک کے بارے میں
A calculator can carry more digits than a measured result can justify. These 48 significant figures flashcards practice reporting short mixed-operation calculations while keeping the carried value separate from its reporting limit.
The deck includes six foundations, ten addition/subtraction-before-multiplication/division calculations, ten multiplication/division-before-addition/subtraction calculations, eight handoff decisions, eight mistake repairs, and six exact-input or evidence-limit prompts. Calculation fronts ask for one final reported answer. Handoff fronts map a supplied carried value and stated limit to the count or decimal place needed next. Repair fronts ask for one corrected final report, count, place, or carried numerator. Exact-input cards practice defined factors and counts; evidence cards ask whether digit reporting establishes accuracy, an uncertainty distribution, or instrument calibration.
Use the ordinary introductory classroom approximation: follow operation order, keep unrounded numerical values, track each reporting limit separately, and round only the final report. Inputs are measured unless a card explicitly marks them exact. Abstract arithmetic exercises omit units; the mass-average example uses compatible gram units. Scientific notation and decimal trailing zeros make retained precision explicit, including cases where rounding changes the magnitude.
The sequence starts with the two operation rules, meaningful zeros, exact counts, and the two-ledger method. It then interleaves calculations, handoffs, repairs, and evidence limits. Two-bracket calculations and final magnitude-change calculations come later. Closely related variants have at least three unrelated cards between them; long-term spacing belongs to the review scheduler.
You should already be able to do ordinary arithmetic. This is focused reporting-precision practice, not a complete chemistry course or exam deck. It excludes logarithms and pH, powers and roots, exact halfway ties, zero-result cancellation, negative-number rounding, medical arithmetic, imperial conversions, and full uncertainty propagation because those need additional conventions or a different task. It also omits a broad digit-counting glossary, long worksheets, and mechanical reversals of calculations: a final answer does not uniquely recover its inputs.
The classroom conventions were checked against Gonzaga’s CHEM 101 guidance and Newfoundland and Labrador’s scientific conventions. The evidence limits were checked against OpenStax’s measurement guidance and NIST’s measurement-uncertainty discussion. Every expression, number choice, question, explanation, and arrangement was independently authored; no source exercises, competitor cards, or examination material were copied or adapted.
AI tools drafted and sequenced the cards and generated the decorative cover. Every final front and back was manually read and solved during author review, with a separate arithmetic and reporting-limit ledger; the cover was checked at full size and across anticipated crops. No learner testing or professional credential is claimed. The original questions, answers, organization, metadata, and generated cover are shared under CC0 1.0 to the extent applicable rights exist. The underlying facts remain common knowledge, and referenced sources retain their own rights. This is independent, unofficial study practice with no affiliation to the cited organizations or claimed curriculum alignment.
اس ڈیک کے کارڈز
کارڈ 1
سوال
In introductory significant-figure arithmetic, which reporting limit governs adding or subtracting measured values in compatible units?
جواب
The coarsest last reported place among the inputs
Track a decimal place, such as tenths or hundredths, rather than taking the smallest significant-figure count.
کارڈ 2
سوال
Which reporting limit governs multiplying or dividing measured values under introductory significant-figure rules?
جواب
The smallest significant-figure count among the measured inputs
An explicitly exact count or defined factor does not impose a finite count limit.
کارڈ 3
سوال
A measured value is written as 0.0460. How many significant figures does that notation retain?
جواب
Three
The leading zeros locate the decimal point. The final zero retains the ten-thousandths place; it is significant.
کارڈ 4
سوال
Exactly 8 identical portions are counted. Does that count restrict a calculation to one significant figure?
جواب
No
An exact count has no finite significant-figure limit. Measured quantities still constrain the result.
کارڈ 5
سوال
What two records should you keep for an intermediate result in a mixed-operation significant-figure calculation?
جواب
Its unrounded carried value and its reporting limit
Use the carried value in the next calculation. Keep the allowed count or decimal place separately, and round only the final report.
کارڈ 6
سوال
At a change from addition to multiplication, how do you find the intermediate sum’s significant-figure count without rounding the value you carry?
جواب
Count the digits in its reportable form at the sum’s allowed place
That form determines the next count limit; the unrounded sum remains the numerical input. Extra calculator digits do not add measured precision.
کارڈ 7
سوال
Report
(8.4 + 2.17) × 3.62using introductory significant-figure rules. These are measured inputs in an abstract arithmetic exercise; units are omitted.جواب
38.3
Carry the sum 10.57 and product 38.2634. The sum is limited to tenths (reportable as 10.6, three figures); 3.62 also has three figures, so report three.
کارڈ 8
سوال
Report
2.46 × 3.1 + 0.842. Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
8.5
Carry the product 7.626 and sum 8.468. The product has a two-figure limit (7.6), whose last place is tenths. That is coarser than the addend’s thousandths, so the final sum ends at tenths.
کارڈ 9
سوال
A measured sum is carried as 0.0827 with a thousandths reporting limit. How many figures may that sum contribute to a following multiplication?
جواب
Two
Its reportable form is 0.083. Use that two-figure limit while carrying 0.0827 numerically.
کارڈ 10
سوال
Report
(15.83 − 4.2) ÷ 2.74. Use introductory significant-figure rules; inputs are measured and units are omitted for this abstract exercise.جواب
4.24
Carry 11.63 through the division: 11.63/2.74 = 4.244525547…. The difference has a tenths limit (11.6, three figures); the divisor has three figures. Report three.
کارڈ 11
سوال
A calculated measured result is correctly reported as 12.30 under significant-figure rules. Does that notation establish that it is close to the true value?
جواب
No
It states a reporting limit, here four figures ending at hundredths. Accuracy needs evidence about the measurement and a suitable reference; retained digits alone do not provide it.
کارڈ 12
سوال
For
(2.8 + 0.146) × 6.63, a student substitutes 2.9 for the sum and reports 1.9 × 10¹. What final report follows from carrying the unrounded sum? Use introductory rules; measured abstract inputs, units omitted.جواب
2.0 × 10¹
Carry 2.946, giving 19.53198. The sum has a tenths limit (2.9, two figures), so the final report has two figures. Substituting 2.9 early changes the carried product to 19.227 and changes the final rounding.
کارڈ 13
سوال
Report
0.0374 × 2.6 + 0.00418. Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
0.101
Carry product 0.09724 and sum 0.10142. The product’s two-figure form is 0.097, ending at thousandths. The final addition uses that place, even though 0.101 has three figures.
کارڈ 14
سوال
A measured product is carried as 63.784 with a three-figure reporting limit. What last place does it contribute to a following addition?
جواب
Tenths
Its three-figure form is 63.8. Keep 63.784 in the numerical calculation; use tenths in the addition’s limit ledger.
کارڈ 15
سوال
Report
(6.28 − 5.9) × 7.43. Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
3
The difference is carried as 0.38, with a tenths limit (reportable as 0.4, one figure). The unrounded product is 2.8234; its one-figure limit gives 3.
کارڈ 16
سوال
Report
(6.27 + 0.46) ÷ 3, where 3 is an explicitly exact defined divisor and the other inputs are measured. Use introductory rules; abstract arithmetic, units omitted.جواب
2.24
Carry sum 6.73 and quotient 2.243333333…. The sum’s hundredths limit gives three figures. The exact divisor imposes no finite limit, so retain three.
کارڈ 17
سوال
Report
18.24 ÷ 4.2 − 0.316. Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
4.0
Carry the quotient 4.342857142… and difference 4.026857142…. Two figures make the quotient reportable as 4.3, ending at tenths. The subtraction therefore ends at tenths; keep the zero in 4.0.
کارڈ 18
سوال
A student reports
3.26 × 1.7 + 0.024as 5.566. What final report corrects the excess digits? Use introductory rules; measured abstract inputs, units omitted.جواب
5.6
Carry product 5.542 and sum 5.566. The product is limited to two figures (5.5, tenths), so the final addition ends at tenths.
کارڈ 19
سوال
A student assigns two significant figures to
(14.2 − 0.87) × 2.36by choosing the smallest count anywhere in the expression. What final figure count should replace that choice? Use introductory rules; measured abstract inputs, units omitted.جواب
Three
Carry the difference 13.33 and product 31.4588. Subtraction gives a tenths limit (13.3, three figures), then multiplication uses three figures from each input. The final report is 31.5.
کارڈ 20
سوال
Report
7 × (1.83 + 0.4), where 7 is an explicitly exact defined multiplier and the other inputs are measured. Use introductory significant-figure rules; abstract arithmetic, units omitted.جواب
1.6 × 10¹
Carry sum 2.23 and product 15.61. The sum has a tenths limit (2.2, two figures). The exact multiplier does not reduce that count, so report two figures.
کارڈ 21
سوال
Report
7.82 ÷ 3.46 + 1.7. Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
4.0
Carry quotient 2.260115606… and sum 3.960115606…. The quotient’s three-figure form, 2.26, ends at hundredths. The measured addend 1.7 sets the coarser tenths limit.
کارڈ 22
سوال
A measured quotient is carried as 0.009974 with a two-figure limit. What last place does it contribute to a following addition?
جواب
Thousandths
Its two-figure form is 0.010. The last retained zero is in the thousandths place after rounding changes the magnitude; carry 0.009974.
کارڈ 23
سوال
For
24.81 + 2.3 × 1.4, a student applies a two-significant-figure limit to the final addition. Which decimal place should govern that addition instead? Use introductory rules; measured abstract inputs, units omitted.جواب
Tenths
Carry product 3.22 and sum 28.03. The product’s two-figure form is 3.2, ending at tenths, which is coarser than 24.81’s hundredths. The final report is 28.0.
کارڈ 24
سوال
Report
(0.0631 + 0.008) × 4.26. Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
0.30
Carry the sum 0.0711 and product 0.302886. The sum’s thousandths limit gives 0.071, two figures. The product is therefore limited to two figures; the final zero in 0.30 matters.
کارڈ 25
سوال
Report
4 × (2.746 − 0.18), where 4 is an explicitly exact defined multiplier and the other inputs are measured. Use introductory rules; abstract arithmetic, units omitted.جواب
10.3
Carry difference 2.566 and product 10.264. The difference has a hundredths limit (2.57, three figures). The exact factor leaves a three-figure final limit.
کارڈ 26
سوال
A measured sum is carried as 9.962 with a tenths reporting limit. How many figures does it contribute to a following multiplication?
جواب
Three
At tenths, its reportable form is 10.0, with three figures. Carry 9.962 rather than replacing it with 10.0.
کارڈ 27
سوال
Report
(42.6 + 1.384) ÷ 6.237. Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
7.05
Carry 43.984 into the quotient, giving 7.052108385…. The sum has a tenths limit: 44.0 retains three figures. The divisor has four, so report three.
کارڈ 28
سوال
A student reports
12.83 × 3.2 + 0.274as 41.3. What final report follows from the product’s proper handoff limit? Use introductory rules; measured abstract inputs, units omitted.جواب
41
Carry product 41.056 and sum 41.330. The product has two figures (41), ending at units. The final sum must also end at units.
کارڈ 29
سوال
Report
23.4 × 6.1 − 2.38. Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
1.4 × 10²
Carry product 142.74 and difference 140.36. The product’s two-figure form is 1.4 × 10², ending at tens. The final subtraction also ends at tens; scientific notation makes that limit clear.
کارڈ 30
سوال
Can a significant-figure count alone determine a measured input’s statistical uncertainty distribution?
جواب
No
These classroom rules approximate how to report digits. An uncertainty model needs measurement information; the count does not specify a distribution or perform uncertainty propagation.
کارڈ 31
سوال
Report
(1.806 − 0.73) ÷ 0.4821. Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
2.23
Carry the difference 1.076; the quotient is 2.231902095…. The difference’s hundredths limit gives 1.08, three figures, which limits the final division.
کارڈ 32
سوال
A measured product is carried as 98.76 with a two-figure limit. What last place does it contribute to a following subtraction?
جواب
Units
Its reportable form is 99. Carry 98.76, but use the units place when comparing the addends’ reporting limits.
کارڈ 33
سوال
A student reports
0.028 × 4.316 + 0.0034as 0.1242, using four calculator digits from the product. What final report corrects that choice? Use introductory rules; measured abstract inputs, units omitted.جواب
0.12
Carry product 0.120848 and sum 0.124248. The product has a two-figure limit (0.12), ending at hundredths. That place governs the addition.
کارڈ 34
سوال
Measured masses 7.31 g, 8.42 g and 9.16 g are averaged by dividing their sum by an exact count of 3. A student lets that count impose a one-figure limit. What figure count should replace it under the introductory sum-then-division rules?
جواب
Four
Carry sum 24.89 g and quotient 8.296666666… g. The sum’s hundredths limit gives four figures; the exact divisor adds no limit. These classroom rules give 8.297 g, without supplying a full uncertainty analysis.
کارڈ 35
سوال
Report
(3.47 + 0.2) ÷ (8.16 − 2.05). Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
0.60
Carry numerator 3.67 and denominator 6.11, giving 0.600654664…. The numerator’s tenths limit gives 3.7 (two figures); the denominator has a hundredths limit and three figures. Report two.
کارڈ 36
سوال
Report
0.806 ÷ 2.4 − 0.0127. Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
0.32
Carry quotient 0.335833333… and difference 0.323133333…. Two figures give the quotient a hundredths limit (0.34). That sets the final subtraction’s place.
کارڈ 37
سوال
A measured sum is carried as 102.04 with a units reporting limit. How many figures does it contribute to a following division?
جواب
Three
The units-limited form is 102; its internal zero is significant. Carry 102.04 and use a three-figure limit.
کارڈ 38
سوال
Report
4.72 × 1.83 + 6.4 × 2.1. Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
22
Carry products 8.6376 and 13.44; the sum is 22.0776. Their reportable forms are 8.64 (hundredths) and 13 (units). The final sum ends at units.
کارڈ 39
سوال
Report
(24.8 − 7.16) × (1.42 + 0.083). Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
26.5
Carry 17.64 and 1.503, whose product is 26.51292. Their limits are tenths (17.6, three figures) and hundredths (1.50, three figures). Report the product with three figures.
کارڈ 40
سوال
Report
31.8 ÷ 4.12 − 1.6 × 2.7. Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
3.4
Carry quotient 7.718446601… and product 4.32; the difference is 3.398446601…. Their reportable forms end at hundredths (7.72) and tenths (4.3). The final difference ends at tenths.
کارڈ 41
سوال
For
(9.36 − 8.9) ÷ 0.384, a student enters 0.5 as the numerator after rounding the difference. Which numerical value should be carried as the numerator instead? Use introductory rules; measured abstract inputs, units omitted.جواب
0.46
The unrounded difference is 0.46. Keep its tenths limit separately (reportable as 0.5, one figure). Carrying 0.46 gives quotient 1.197916666… and a one-figure final report of 1.
کارڈ 42
سوال
Report
(2.36 × 10³ + 4.7 × 10²) ÷ 8.214. Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
3.45 × 10²
Carry the sum 2830 and quotient 344.533722912…. Both addends end at the tens place, so the sum is reportable as 2.83 × 10³, three figures. The final quotient retains three.
کارڈ 43
سوال
Report
1.247 × 8.019 + 0.01234. Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
10.01
Carry product 9.999693 and sum 10.012033. The product’s four-figure reportable form is 10.00, ending at hundredths after the magnitude change. That hundredths limit governs the final addition.
کارڈ 44
سوال
A measured product is carried as 0.43821 with a three-figure limit. What last place does it contribute to a following addition?
جواب
Thousandths
Its reportable form is 0.438. The three retained figures reach the thousandths place; carry the full 0.43821.
کارڈ 45
سوال
Report
(0.84 + 0.037) × (3.15 − 0.72). Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
2.1
Carry 0.877 and 2.43; their product is 2.13111. The sum’s hundredths limit gives 0.88, two figures. The difference has three figures, so report two.
کارڈ 46
سوال
A measured difference is carried as 0.146 with a hundredths reporting limit. What figure count does it contribute to a following division?
جواب
Two
Its reportable form is 0.15, which has two figures. The subtraction’s place limit does not preserve the original operands’ digit counts.
کارڈ 47
سوال
Every calculation in a lab report obeys significant-figure rules. Does that establish that the instrument was correctly calibrated?
جواب
No
Digit reporting cannot detect a systematic calibration error. Calibration requires independent checks against appropriate references.
کارڈ 48
سوال
Report
9.984 ÷ 1.001 + 0.0362. Use introductory significant-figure rules; measured abstract inputs, units omitted.جواب
10.010
Carry quotient 9.974025974… and sum 10.010225974…. The quotient’s four-figure form is 9.974, ending at thousandths. Addition keeps that place even after crossing 10, so the final report has five figures.
48 کارڈز
Significant Figures Flashcards: Mixed Operations & Rounding
مطالعہ شروع کرنے کے لیے Nibomo کھلے گا۔