Characteristic and Mantissa MCQs With Answer

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Understanding Characteristic and Mantissa MCQs With Answer is essential for B. Pharm students tackling pharmaceutical calculations and log-based problems. This focused set explains how the characteristic (the integer part) and the mantissa (the positive fractional part) of common logarithms work, how to use log tables, compute antilogs, and apply rules for numbers greater or less than one. Emphasis is placed on practical examples in dosage calculations, concentration and pH estimations, significant figures, and using mantissa shortcuts to speed calculations. Clear definitions, rules and practice MCQs help build accuracy and confidence in logarithmic manipulation for pharmacy coursework. Now let’s test your knowledge with 50 MCQs on this topic.

Q1. What is the definition of the characteristic in a common logarithm?

  • The integer part of the base-10 logarithm
  • The fractional part of the natural logarithm
  • The antilog value of a number
  • The exponent of e in natural logs

Correct Answer: The integer part of the base-10 logarithm

Q2. What does the mantissa represent in a base-10 logarithm?

  • The positive fractional part of the common logarithm
  • The negative integer part of the logarithm
  • The absolute value of the characteristic
  • The logarithm base

Correct Answer: The positive fractional part of the common logarithm

Q3. For log10(250), what is the characteristic?

  • 2
  • 1
  • 3
  • 0

Correct Answer: 2

Q4. For log10(0.025), what is the characteristic?

  • -2
  • -1
  • 0
  • -3

Correct Answer: -2

Q5. Which statement about mantissa is correct?

  • Mantissa is always positive for common logs
  • Mantissa can be negative for numbers < 1
  • Mantissa equals the characteristic for powers of 10
  • Mantissa is always zero except for irrational numbers

Correct Answer: Mantissa is always positive for common logs

Q6. log10(1000) equals 3. What is the mantissa?

  • 0
  • 1
  • 3
  • 10

Correct Answer: 0

Q7. If log10(7) ≈ 0.8451, what is the characteristic and mantissa for log10(0.7)?

  • Characteristic -1, Mantissa 0.8451
  • Characteristic 0, Mantissa 0.8451
  • Characteristic -1, Mantissa -0.8451
  • Characteristic 1, Mantissa 0.8451

Correct Answer: Characteristic -1, Mantissa 0.8451

Q8. How do you obtain the mantissa of 0.0035 using properties of logs?

  • Find mantissa of 3.5 and use same mantissa with characteristic -3
  • Mantissa equals -log10(0.0035)
  • Divide 0.0035 by 10 until it exceeds 1 and take that quotient as mantissa
  • Use natural log instead of common log

Correct Answer: Find mantissa of 3.5 and use same mantissa with characteristic -3

Q9. Which of the following ranges corresponds to characteristic -2?

  • 0.01 ≤ N < 0.1
  • 0.001 ≤ N < 0.01
  • 0.1 ≤ N < 1
  • 1 ≤ N < 10

Correct Answer: 0.01 ≤ N < 0.1

Q10. If log10(2) ≈ 0.3010, what is log10(0.2)?

  • -0.6990
  • -0.3010
  • -1 + 0.3010 = -0.6990
  • 0.3010

Correct Answer: -1 + 0.3010 = -0.6990

Q11. Which rule helps find mantissa for numbers like 0.045?

  • Use mantissa of 4.5 and assign characteristic -2
  • Use mantissa of 45 and assign characteristic -1
  • Use square root of mantissa of 45
  • Mantissa is simply the decimal digits after zero

Correct Answer: Use mantissa of 4.5 and assign characteristic -2

Q12. For a number 8.2, if log10(8.2)=0.9138, what is mantissa and characteristic?

  • Characteristic 0, Mantissa 0.9138
  • Characteristic 1, Mantissa 0.9138
  • Characteristic 0, Mantissa -0.9138
  • Characteristic 1, Mantissa -0.9138

Correct Answer: Characteristic 0, Mantissa 0.9138

Q13. Which is true about mantissa when using log tables for numbers >1?

  • Lookup mantissa using the significant digits as if the number were normalized between 1 and 10
  • Mantissa is read directly from the characteristic column
  • Mantissa equals the integer part of the number
  • Mantissa is negative for numbers >1

Correct Answer: Lookup mantissa using the significant digits as if the number were normalized between 1 and 10

Q14. How is an antilog of a number with characteristic 2 and mantissa 0.3010 interpreted?

  • 10^(2.3010) ≈ 200
  • 10^(0.3010) ≈ 2
  • 10^(2.3010) ≈ 2
  • 10^(0.3010) ≈ 20

Correct Answer: 10^(2.3010) ≈ 200

Q15. For pharmaceutical calculations, why is understanding mantissa useful?

  • It speeds multiplication/division using log tables and antilogs
  • It replaces the need for units in dosage calculations
  • It eliminates errors due to rounding completely
  • It only applies to natural logarithms

Correct Answer: It speeds multiplication/division using log tables and antilogs

Q16. If log10(50) ≈ 1.6990, what is the mantissa?

  • 0.6990
  • 1.6990
  • 0.3010
  • 1.3010

Correct Answer: 0.6990

Q17. Which is the correct characteristic for 0.0007?

  • -4
  • -3
  • -2
  • -1

Correct Answer: -4

Q18. If mantissa for 6 is 0.77815, what is log10(0.6)?

  • -0.22185
  • -1 + 0.77815 = -0.22185
  • 0.77815
  • -0.77815

Correct Answer: -1 + 0.77815 = -0.22185

Q19. Which method converts a number to a form suitable for log tables?

  • Normalize the number between 1 and 10 and adjust characteristic by powers of 10
  • Convert to natural log directly
  • Divide the number by its characteristic
  • Square the number then take log

Correct Answer: Normalize the number between 1 and 10 and adjust characteristic by powers of 10

Q20. If log10(x)= -2 + 0.3010, what is x approximately?

  • 0.002
  • 0.002 = 10^(-1.699) so approximately 0.002
  • 0.2
  • 2

Correct Answer: 0.002 = 10^(-1.699) so approximately 0.002

Q21. In log table lookup, what digits determine mantissa entry?

  • First four significant digits of the normalized number
  • Only the last two digits of the original number
  • The integer part of the original number
  • Number of zeros preceding the first digit

Correct Answer: First four significant digits of the normalized number

Q22. Which is true for the mantissa of a number and its multiples by powers of 10?

  • The mantissa remains the same when multiplied or divided by powers of 10
  • The mantissa reverses sign when multiplied by 10
  • The mantissa doubles when multiplied by 100
  • The mantissa becomes zero for any power of 10

Correct Answer: The mantissa remains the same when multiplied or divided by powers of 10

Q23. For pH calculation, pH = -log10[H+]. If [H+] = 3.2 × 10^-5, what is characteristic of -log10[H+]?

  • 4
  • -5
  • -4
  • 5

Correct Answer: 4

Q24. If log10(9) ≈ 0.9542, what is log10(0.09)?

  • -2 + 0.9542 = -1.0458
  • -1 + 0.9542 = -0.0458
  • 0.9542
  • -0.9542

Correct Answer: -2 + 0.9542 = -1.0458

Q25. Which of the following is the mantissa of 45?

  • Mantissa of 4.5, because 45 = 4.5 × 10
  • Mantissa of 45 directly from the characteristic column
  • Mantissa is 45
  • Mantissa is zero for two-digit numbers

Correct Answer: Mantissa of 4.5, because 45 = 4.5 × 10

Q26. How do you find antilog given characteristic 1 and mantissa 0.3010?

  • Compute 10^(1.3010) ≈ 20
  • Compute 10^(0.3010) ≈ 2 and ignore characteristic
  • Compute e^(1.3010)
  • Multiply mantissa by 10 and raise to power 1

Correct Answer: Compute 10^(1.3010) ≈ 20

Q27. Which is correct about characteristics of exact powers of 10?

  • Characteristic equals the exponent and mantissa is zero
  • Characteristic is zero and mantissa equals exponent
  • Both characteristic and mantissa are negative
  • Mantissa equals 1 for powers of 10

Correct Answer: Characteristic equals the exponent and mantissa is zero

Q28. If log10(A)=2.3010, what is A approximately?

  • 200
  • 20
  • 2
  • 0.2

Correct Answer: 200

Q29. Which is the correct characteristic for a number between 1 and 10?

  • 0
  • 1
  • -1
  • It depends on mantissa

Correct Answer: 0

Q30. When using log tables for multiplication, how are logs combined?

  • Add logarithms (characteristics and mantissas) then find antilog
  • Subtract mantissas only
  • Multiply mantissas directly
  • Use natural logs instead of common logs

Correct Answer: Add logarithms (characteristics and mantissas) then find antilog

Q31. For the number 0.0042, which of the following is the characteristic and source of mantissa?

  • Characteristic -3; mantissa same as for 4.2
  • Characteristic -4; mantissa same as for 42
  • Characteristic -2; mantissa same as for 0.42
  • Characteristic -3; mantissa negative of 4.2

Correct Answer: Characteristic -3; mantissa same as for 4.2

Q32. If log10(3.162) ≈ 0.4997, what is log10(31.62)?

  • 1.4997
  • 0.4997
  • 2.4997
  • -0.5003

Correct Answer: 1.4997

Q33. Which practice speeds error-free use of log tables in exams?

  • Normalize numbers and track characteristic changes carefully
  • Ignore characteristic and focus only on mantissa
  • Always round mantissa to nearest integer before lookup
  • Use logs only for integers

Correct Answer: Normalize numbers and track characteristic changes carefully

Q34. If mantissa of 7.5 is 0.8751 (approx), what is log10(0.075)?

  • -2 + 0.8751 = -1.1249
  • -1 + 0.8751 = -0.1249
  • 0.8751
  • -0.8751

Correct Answer: -2 + 0.8751 = -1.1249

Q35. When adding logarithms, how do you treat characteristics and mantissas?

  • Add characteristics and mantissas, adjust if mantissa ≥1 by increasing characteristic
  • Only add mantissas and ignore characteristics
  • Subtract characteristics and add mantissas
  • Multiply characteristics and mantissas separately

Correct Answer: Add characteristics and mantissas, adjust if mantissa ≥1 by increasing characteristic

Q36. Which of the following is a correct mantissa equality?

  • Mantissa(log10(0.56)) = Mantissa(log10(5.6))
  • Mantissa(log10(0.56)) = -Mantissa(log10(5.6))
  • Mantissa(log10(0.56)) = Mantissa(log10(56)) + 1
  • Mantissa values are unrelated for such numbers

Correct Answer: Mantissa(log10(0.56)) = Mantissa(log10(5.6))

Q37. A B. Pharm student uses log tables to compute (2.5 × 10^3) × (4 × 10^-2). Which is correct approach?

  • Add logs of 2.5 and 4, then add exponents (3 and -2) to get overall exponent then antilog
  • Multiply mantissas directly without logs
  • Add the original numbers then take log
  • Use natural logs only

Correct Answer: Add logs of 2.5 and 4, then add exponents (3 and -2) to get overall exponent then antilog

Q38. Which statement about negative characteristics is correct?

  • Negative characteristics reflect numbers less than 1 and mantissa remains positive
  • Negative characteristics make mantissa negative too
  • Negative characteristics indicate an error in normalization
  • Negative characteristics only occur for integers

Correct Answer: Negative characteristics reflect numbers less than 1 and mantissa remains positive

Q39. If log10(12) ≈ 1.0792, what is the mantissa used for 0.12?

  • 0.0792 with characteristic -1 adjusted to 0.0792
  • 1.0792
  • 0.9208
  • -0.0792

Correct Answer: 0.0792 with characteristic -1 adjusted to 0.0792

Q40. Which of the following helps check antilog calculations quickly?

  • Verify that mantissa corresponds to normalized significant digits and characteristic gives scale
  • Ensure mantissa is larger than characteristic
  • Confirm characteristic is always positive
  • Compare to natural log tables

Correct Answer: Verify that mantissa corresponds to normalized significant digits and characteristic gives scale

Q41. When converting 4500 to normalized form for log lookup, what is the normalized number?

  • 4.5 × 10^3
  • 45 × 10^2
  • 0.45 × 10^4
  • 450 × 10^1

Correct Answer: 4.5 × 10^3

Q42. If mantissa table gives 0.6021 for 4.0, what is log10(40)?

  • 1.6021
  • 0.6021
  • 2.6021
  • -0.3979

Correct Answer: 1.6021

Q43. In pharmacy, how can mantissa help with dilution calculations?

  • Logs convert multiplication/division of concentrations to addition/subtraction, simplifying dilutions
  • Mantissa directly gives dilution factor without calculations
  • Mantissa replaces concentration units
  • Mantissa only applies to solid dosage forms

Correct Answer: Logs convert multiplication/division of concentrations to addition/subtraction, simplifying dilutions

Q44. For the number 0.5, which is correct log decomposition?

  • log10(0.5) = -1 + 0.3010
  • log10(0.5) = 0.3010
  • log10(0.5) = -0.3010
  • log10(0.5) = 1 – 0.3010

Correct Answer: log10(0.5) = -1 + 0.3010

Q45. Which property is useful: mantissa(AB) where A and B are normalized between 1 and 10?

  • mantissa(log A + log B) = mantissa of log(A×B), with carry to characteristic if needed
  • Mantissa of product equals sum of mantissas without any adjustment
  • Mantissa of product equals product of mantissas
  • Mantissa cannot be used for product calculations

Correct Answer: mantissa(log A + log B) = mantissa of log(A×B), with carry to characteristic if needed

Q46. If log10(20)=1.3010, what is mantissa and characteristic?

  • Characteristic 1, Mantissa 0.3010
  • Characteristic 0, Mantissa 1.3010
  • Characteristic 2, Mantissa 0.3010
  • Characteristic 1, Mantissa 1.3010

Correct Answer: Characteristic 1, Mantissa 0.3010

Q47. Which is the mantissa of 0.00032 based on normalization?

  • Mantissa same as 3.2 (0.5051 approx for 3.2)
  • Mantissa same as 32
  • Mantissa is -3
  • Mantissa equals number of zeros

Correct Answer: Mantissa same as 3.2 (0.5051 approx for 3.2)

Q48. For accurate use of log tables, which rounding practice is recommended?

  • Carry sufficient significant figures in mantissa and round only at final antilog
  • Round mantissa to integer values early
  • Always truncate mantissa to two decimals
  • Ignore rounding since mantissa handles precision

Correct Answer: Carry sufficient significant figures in mantissa and round only at final antilog

Q49. If log10(0.9) = -0.0458 approximately, what are characteristic and mantissa?

  • Characteristic -1, Mantissa 0.9542
  • Characteristic 0, Mantissa -0.0458
  • Characteristic -1, Mantissa 0.0458
  • Characteristic 0, Mantissa 0.9542

Correct Answer: Characteristic -1, Mantissa 0.9542

Q50. Which summarizes why mantissa remains identical for 3.5, 35, 0.35, and 350?

  • Multiplying/dividing by powers of 10 only changes characteristic; mantissa depends on significant digits
  • Mantissa depends on the absolute magnitude, so it remains identical
  • Characteristic and mantissa always change together
  • Because logs are linear only for integers

Correct Answer: Multiplying/dividing by powers of 10 only changes characteristic; mantissa depends on significant digits

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