Convention
Bar notation for a negative characteristic
Algebra • Logarithm • Characteristic and Mantissa
Formula
A common logarithm is written as a characteristic plus a mantissa, with the mantissa always kept in ; when the logarithm is negative the minus sign is carried by the characteristic alone and marked with a bar, so denotes .
How to use it
- 1To put a negative decimal into bar form, take it up to the next whole number: .
- 2To read a bar form back, add the negative whole part to the positive decimal: .
- 3Keeping the mantissa positive is what lets one antilogarithm table serve every number; the characteristic only says where the decimal point goes.
Worked example
Write in bar notation.
Step-by-step
- 1
Why: Go down to the next whole number, , so that what is left over is positive.
- 2
Answer
Watch out
is , not : the bar covers the whole part only. Addition must carry out of the mantissa into the characteristic - has mantissa sum , so the carried lifts to and the answer is .
Builds on
Also known as
bar notation, negative characteristic, mantissa always positive, one bar point, log of a number less than 1, characteristic with a bar