Q.Write any two rules for determining significant figures.
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🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Significant Figures
Significant figures are the digits in a measurement that are known reliably, plus the first uncertain one. They are how a number honestly advertises its own precision: writing a length as 2.50 m claims more than 2.5 m, because the trailing zero says the hundredths place was actually measured. Two skills live here — counting the significant figures a number already carries, and not manufacturing precision when you compute with them.
1 — The least count sets the precision. Every instrument can resolve only down to its least count (LC) — the smallest division it can read. A metre scale marked in millimetres has LC = 1 mm; a vernier calliper has LC = 1 MSD − 1 VSD (equivalently 1 MSD / n when n vernier divisions span n−1 main divisions), typically 0.1 mm; a screw gauge / micrometer has LC = pitch / (number of circular-scale divisions), typically 0.01 mm. A measurement is read as main-scale reading + (coinciding division × LC), corrected for any zero error (a non-zero reading when the jaws are closed: a positive zero error is subtracted, a negative one is added).
2 — Counting significant figures. The rules: (i) every non-zero digit is significant; (ii) zeros between non-zero digits are significant (3.05 → 3 s.f.); (iii) leading zeros are never significant — they only fix the decimal point (0.0047 → 2 s.f.); (iv) trailing zeros are significant only if there is a decimal point (4.50 → 3 s.f., but 4500 is ambiguous); (v) scientific notation removes the ambiguity — 4.5 × 10³ shows 2 s.f., 4.50 × 10³ shows 3. A change of unit never changes the count: 5.60 cm and 0.0560 m both have 3 s.f.
3 — Rounding. To round to a required number of significant figures or decimal places: if the first dropped digit is > 5 round up, < 5 round down, and for exactly 5 the common convention rounds up (some texts round to the nearest even digit — state which you use). Rounding to N significant figures and to N decimal places are different operations — don't confuse them.
4 — Arithmetic doesn't create precision. The result of a calculation can be no more precise than its least-precise input. Addition and subtraction: the result keeps the least number of decimal places among the operands (12.3 + 4.56 = 16.9, one decimal). Multiplication and division: the result keeps the least number of significant figures (2.5 × 3.42 = 8.6, two s.f.). The classic trap is applying the wrong rule — using least-significant-figures on a sum, or least-decimals on a product. …
Two common rules for determining significant figures: (1) All non-zero digits are significant (e.g., in 245, all 3 digits are significant); (2) All zeros occurring between two non-zero digits are significant (e.g., in 1005, all 4 digits, including the zeros, are significant). …
Two standard rules: all non-zero digits are significant, and zeros sandwiched between non-zero digits (captive zeros) are also significant.
Significant figures are the digits in a measured (or calculated) quantity that are known reliably, plus one estimated (uncertain) digit. The following are two of the standard rules used to count them:
Rule 1 — All non-zero digits are significant.
Example: In the number 4257, all four digits (4, 2, 5, 7) are non-zero, so all four are significant figures.
Rule 2 — All zeros occurring between two non-zero digits (captive/embedded zeros) are significant.
Example: In the number 1002, the two zeros lie between the non-zero digits 1 and 2, so the number has 4 significant figures. Similarly, 3.05 has 3 significant figures (the zero between 3 and 5 counts).
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Showing the 12 most recent of 13 on this concept.
- CBSE 2026Set ANNUAL1 markMCQQ.The significant figures of number 20340 are :(a) 3(b) 4(c) 5(d) 1
›Reveal solutionSolution
20340 has 4 significant figures: the trailing zero after the last non-zero digit is not counted as significant when there is no decimal point.
Rules for counting significant figures:
- All non-zero digits are significant.
- Zeros between two non-zero digits are significant.
- Trailing zeros in a number with no decimal point are NOT significant — they only fix the position of the decimal point / order of magnitude.
Applying this to 20340:
- 2 → significant …
- CBSE 2026Set sz1 markMCQQ.The number of significant figures in 6638 is:(a) 1(b) 2(c) 3(d) 4
›Reveal solutionSolution
All non-zero digits in a measured number are significant, so 6638 has 4 significant figures.
The rules for counting significant figures state that all non-zero digits are significant. In the number 6638, the digits are 6, 6, 3, and 8 — …
- CBSE 2026Set ANNUAL1 markQ.Write the answer in one word/one sentence: How many significant digits are there in the number 0.03000?
›Reveal solutionSolution
0.03000 has 4 significant figures: the '3' and the three trailing zeros after it.
Rules for counting significant figures:
- All non-zero digits are significant.
- Zeros between non-zero digits are significant.
- Leading zeros (before the first non-zero digit) are NOT significant — they only fix the position of the decimal point.
- Trailing zeros after a decimal point ARE significant, because they indicate the precision to which the quantity was measured.
In 0.03000: …
- CBSE 2026Set ANNUAL1 markMCQQ.The numbers of significant digits in 0.0065 and 2.0065 are respectively(a) 4, 5(b) 2, 3(c) 4, 3(d) 2, 5
›Reveal solutionSolution
0.0065 -> 2 significant figures; 2.0065 -> 5 significant figures. Answer (D).
Rules for significant figures:
- Leading zeros (zeros only used to fix the decimal point) are NOT significant.
- Zeros trapped between non-zero digits ARE significant. …
- CBSE 2025Set ANNUAL1 markMCQQ.A cube has a side of length 1.2 x 10^-2 m. Its volume up to correct significant figures is(a) 1.7 x 10^-6 m^3(b) 1.73 x 10^-6 m^3(c) 1.78 x 10^-6 m^3(d) 1.732 x 10^-6 m^3
›Reveal solutionSolution
Volume = side^3 = 1.728 x 10^-6 m^3, but since the given length has only 2 significant figures, the answer must be rounded to 2 sig figs: 1.7 x 10^-6 m^3.
Side of cube, a = 1.2 x 10^-2 m. This value has exactly 2 significant figures (the digits 1 and 2).
Volume V = a^3 = (1.2 x 10^-2)^3 = 1.728 x 10^-6 m^3 (raw calculator value).
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- CBSE 2025Set ANNUAL1 markMCQQ.State the number of significant figures in 0.06900(a) 1(b) 2(c) 4(d) 3
›Reveal solutionSolution
0.06900 has 4 significant figures.
Rules for counting significant figures: all non-zero digits are significant; zeros between non-zero digits are significant; leading zeros (before the first non-zero digit) are NEVER significant — they only locate the decimal point; trailing zeros after the decimal point, once a non-zero digit has appeared, ARE significant (they show measurement precision).
In 0.06900:
- The zeros before the 6 (0.0) are leading zeros → not significant. …
- CBSE 2025Set hz1 markMCQQ.The number of significant figures in 2.64 x 10^24 Kg is:(a) 3(b) 4(c) 24(d) 1
›Reveal solutionSolution
Only the digits actually measured count as significant; a power-of-ten multiplier in scientific notation is never counted. 2.64 x 10^24 kg has 3 significant figures.
When a number is written in scientific notation as N x 10^n, the significant figures are exactly the digits in N (the coefficient), regardless of how large or small the exponent n is. This convention exists precisely so that changing units (which changes only the exponent) never changes how precisely a quantity is known.
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- CBSE 2025Set ANNUAL1 markMCQQ.The number of significant figures for 6.0023g cm−3 is(a) 5(b) 3(c) 1(d) 4
›Reveal solutionSolution
In 6.0023 g cm−3, every digit — 6, 0, 0, 2, 3 — is significant because zeros lying between two non-zero digits are always counted as significant figures.
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- CBSE 2025Set sz1 markMCQQ.The numbers 2.745 and 2.735 on rounding off to 3 significant figures will give: (A) 2.75 and 2.74 (B) 2.74 and 2.73 (C) 2.75 and 2.73 (D) 2.74 and 2.74
›Reveal solutionSolution
Using the round-half-to-even rule, both 2.745 and 2.735 round to 2.74 to three significant figures.
Rounding to 3 significant figures here means keeping two decimal places. The dropped digit is 5 in both numbers, so the special rule applies: raise the preceding digit by 1 if it is odd, leave it unchanged if it is even. …
- CBSE 2024Set sz1 markMCQQ.The number of significant numbers in 23.023 is: (A) 2 (B) 3 (C) 4 (D) 5
›Reveal solutionSolution
23.023 has 5 significant figures — every digit counts because the internal zero is sandwiched between non-zero digits.
Rules for counting significant figures: (1) all non-zero digits are significant, (2) zeros between two non-zero digits are significant, (3) leading zeros are never significant, (4) trailing zeros after a decimal point are significant.
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- CBSE 2022Set ANNUAL1 markMCQQ.The number of significant figures in 0.007 m2 is(a) 1(b) 3(c) 4(d) 7
›Reveal solutionSolution
0.007 m2 has only 1 significant figure — the digit 7.
Significant figures are the digits in a measurement that carry real information about its precision. The rule for zeros is: zeros that appear before the first non-zero digit (leading zeros) are never significant — they only locate the decimal point and depend on the choice of unit, not on measurement precision.
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- CBSE 2019Set hz1 markQ.What is the number of significant digits in 0.005 m^2 ?
›Reveal solutionSolution
Leading zeros are never significant, so 0.005 m^2 has exactly 1 significant figure.
Rules for significant figures:
- All non-zero digits are significant.
- Zeros between two non-zero digits are significant.
- Leading zeros (to the left of the first non-zero digit) are NOT significant - they only locate the decimal point.
- Trailing zeros after a decimal point ARE significant. …
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