Q.A student measures the length of a rod as 4.700 cm using a vernier caliper of least count 0.01 cm. State the number of significant figures in this measurement and justify the status (certain / uncertain) of each digit.
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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. …
[!TLDR] Count every digit reliably known plus the first uncertain digit. [!ANSWER] $ …
The least count of the vernier caliper is 0.01 cm, so the instrument can reliably resolve the reading down to the second decimal place, with that final digit being the first genuinely uncertain one.
Reading the digits of 4.700 cm in order:
- 4 — the units digit, certain (read directly off the main scale).
- 7 — the first decimal digit, certain (read off the main/vernier scale combination).
- 0 (second decimal) — certain, since the least count resolves to this place. …
Compare the instrument's least count against the last written decimal place, then apply the significant-figure rule that trail …
- Dropping the trailing zeros as 'not meaningful', reading the value as only 2 significant figures …
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).
…
- 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.
…
- 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.
…
- 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.
…
- 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.
…
- 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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