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Characteristic and Mantissa
For a common log, split the value into characteristic (the integer part) and mantissa (the fractional part with 0 <= m < 1). If x = d x 10^n in scientific notation, the characteristic is n. The number of digits in the whole-number part of a number >= 1 is characteristic + 1. A bar over an integer, such as bar 4, means characteristic -4 with a still-positive mantissa. Never write bar 2.0899 as -2.0
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Characteristic and Mantissa
What is it?
For a common log, split the value into characteristic (the integer part) and mantissa (the fractional part with 0 <= m < 1). If x = d x 10^n in scientific notation, the characteristic is n. The number of digits in the whole-number part of a number >= 1 is characteristic + 1. A bar over an integer, such as bar 4, means characteristic -4 with a still-positive mantissa. Never write bar 2.0899 as -2.0899, because that would make the mantissa negative.
In simple words
- For a common log, split the value into characteristic (the integer part) and mantissa (the fractional part with 0 <= m < 1).
- Read n from scientific notation; mantissa stays non-negative: Review each row and apply its rule carefully.
- bar 2 means characteristic -2 with mantissa still between 0 and 1.
Important terms
characteristic: For a common log, split the value into characteristic (the integer part) and mantissa (the fractional part with 0 <= m < 1).
integer part: For a common log, split the value into characteristic (the integer part) and mantissa (the fractional part with 0 <= m < 1).
mantissa: For a common log, split the value into characteristic (the integer part) and mantissa (the fractional part with 0 <= m < 1).
0 <= m < 1: For a common log, split the value into characteristic (the integer part) and mantissa (the fractional part with 0 <= m < 1).
d x 10^n: If x = d x 10^n in scientific notation, the characteristic is n.
What you should learn
- Explain Characteristic And Mantissa in simple mathematical language.
- Read the comparison table and choose the correct rule or method.
- Use the symbols, conditions, and formulae accurately.
- Solve a short example and check the answer.
- Recognise and correct common mistakes.
Recommended for Class 9
Full school-level explanation
For a common log, split the value into characteristic (the integer part) and mantissa (the fractional part with 0 <= m < 1). If x = d x 10^n in scientific notation, the characteristic is n. The number of digits in the whole-number part of a number >= 1 is characteristic + 1. A bar over an integer, such as bar 4, means characteristic -4 with a still-positive mantissa. Never write bar 2.0899 as -2.0899, because that would make the mantissa negative.
WHAT — Core idea
For a common log, split the value into characteristic (the integer part) and mantissa (the fractional part with 0 <= m < 1). If x = d x 10^n in scientific notation, the characteristic is n. The number of digits in the whole-number part of a number >= 1 is characteristic + 1. A bar over an integer, such as bar 4, means characteristic -4 with a still-positive mantissa. Never write bar 2.0899 as -2.0899, because that would make the mantissa negative.
WHY — Why it matters
This idea helps you recognise the right mathematical pattern, choose a safe method, and explain your working clearly.
HOW — Method and examples
720000: 7.2 x 10^5 — 5 (digits in 720000: 6 = 5+1) 4.08: 4.08 x 10^0 — 0 0.00072: 7.2 x 10^-4 — bar 4 (that is -4) 32.5: 3.25 x 10^1 — 1 (2 digits = 1+1) 0.25: 2.5 x 10^-1 — bar 1 1000: 1 x 10^3 — 3
HOW — Answer in an exam
bar 2 means characteristic -2 with mantissa still between 0 and 1. Writing bar 2.0899 as -2.0899 is wrong: -2.0899 would be characteristic -3 plus a positive mantissa 0.9101, or it would look as if the mantissa were negative. Keep the bar only on the integer part.
Remember
- characteristic
- integer part
- mantissa
- 0 <= m < 1
- d x 10^n
- characteristic is n
- characteristic + 1
- bar 4
Deeper understanding
Go beyond memorising Characteristic and Mantissa. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
WHAT
Key Points
HOW
Examples
Exam focus
Quick revision
- characteristic
- integer part
- mantissa
- 0 <= m < 1
- characteristic: For a common log, split the value into characteristic (the integer part) and mantissa (the fractiona
- integer part: For a common log, split the value into characteristic (the integer part) and mantissa (the fractiona
bar 2 means characteristic -2 with mantissa still between 0 and 1. Writing bar 2.0899 as -2.0899 is wrong: -2.0899 would be characteristic -3 plus a positive mantissa 0.9101, or it would look as if the mantissa were negative. Keep the bar only on the integer part.
For long answers on Characteristic and Mantissa: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- characteristic
- integer part
- mantissa
- 0 <= m < 1
Important formulas
- characteristic
- integer part
- mantissa
Common exam traps
- bar 2 means characteristic -2 with mantissa still between 0 and 1.
- Writing bar 2.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
bar 2 means characteristic -2 with mantissa still between 0 and 1.
- Mistake
Writing bar 2.
- Mistake
0899 as -2.
- Mistake
Correction: 0899 is wrong: -2.
- Mistake
bar 2 means characteristic -2 with mantissa still between 0 and 1. Writing bar 2.0899 as -2.0899 is wrong: -2.0899 would be characteristic -3 plus a positive ma
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
characteristic
integer part
mantissa
0 <= m < 1
For a common log, split the value into characteristic (the integer part) and mantissa (the fractional part with 0 <= m < 1). If x = d x 10^n in scientific notat
0 <= m < 1
- Definition
- For a common log, split the value into characteristic (the integer part) and mantissa (the fractional part with 0 <= m < 1). If x = d x 10^n in scientific notat
- Formula
- 0 <= m < 1
- Critical warning
- bar 2 means characteristic -2 with mantissa still between 0 and 1.
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Exam Practice
Define
Q1. Define Characteristic and Mantissa.
Explain
Q2. Explain: WHAT — Core idea.
Example
Q3. Give one clear example of Characteristic and Mantissa and say why it fits.
Mistake
Q4. State one common mistake students make about Characteristic and Mantissa.
Exam note
Q5. Write a short exam note on Characteristic and Mantissa: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.