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Grade 10 · Core Mathematics · Lesson 8 of 13

Reading Common Logarithms in Tables

A Grade 10 Core Mathematics CBE lesson from the sub-strand Indices and Logarithms. In it, learners identify row and column locations in a log table.

Strand Numbers and AlgebraSub-strand Indices and LogarithmsLesson code 10CM-12-L840 minutes · 4 slides

KICD learning outcome (e)

Determine common logarithms of numbers from mathematical tables and calculators.

By the end of this lesson, learners should be able to

  1. Identify row and column locations in a log table.
  2. Combine characteristic and mantissa correctly.
  3. Record table readings with appropriate precision.
  4. Find logarithms of numbers less than 1 using bar notation.

Key vocabulary

Mantissa
The table’s decimal logarithm part after the characteristic.
A mantissa such as 0.4771 supplies precision beyond the characteristic.
Row
A horizontal table location selected by leading digits.
The first two significant digits identify a logarithm-table row.
Characteristic
The integer part floor(log₁₀ N), selected by the exact power-of-ten interval containing N.
The characteristic of 420 is two because 100 ≤ 420 < 1000.
Four-figure table
A logarithm table listing mantissas to four decimal places.
A four-figure table records a mantissa such as 0.7243.
Lookup
Finding a table entry using labelled row and column positions.
The lookup for 7.42 uses row 7.4 and column 2.
Precision
The number of meaningful digits retained in a result.
Recording four mantissa places preserves table precision.

Lesson preview

Slide 1 · Anatomy of a four-figure tableOpening · 10 min
A segment of a common-logarithm table showing how to find the mantissa for 2.36 by intersecting row 2.3 with column 6.
Figure 1: A segment of a common-logarithm table showing how to find the mantissa for 2.36 by intersecting row 2.3 with column 6.

A printed common-logarithm table separates the integer range information from a decimal mantissa. Reading the first significant digits selects a row, the next digit selects a column, and the resulting entry is combined with the characteristic. Use Figure 1 to see how to intersect a row and column to find a mantissa.

  • The characteristic comes from the number’s power-of-ten range.
  • The row uses the leading significant digits.
  • The column supplies the next significant digit.
  • The mantissa is combined after table location is complete.
Worked example. Use 2.3 to choose the row. Use 6 to choose the column. Read the mantissa where that row and column meet. Answer: Row 2.3 and column 6.

Check question: When looking up the mantissa for 8.14 in a common-logarithm table, which row and column pair should be used?

  1. Row 8.1, column 4
  2. Row 8, column 1
  3. Row 8.14, column 0
  4. Row 4, column 8.1
Show answer

Row 8.1, column 4. The first two significant digits (8.1) form the row label, and the third digit (4) selects the column.

Slide 2 · Combine characteristic and mantissaModel · 10 min
A magnitude ladder demonstrating how to find the characteristic of a number and combine it with a mantissa.
Figure 2: A magnitude ladder demonstrating how to find the characteristic of a number and combine it with a mantissa.

Teach the full lesson on the projector

This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

  • All 4 slides with diagrams and class activities
  • Teacher notes, SNE adaptations and assessment checks
  • Homework and the other 12 lessons in this sub-strand
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All 13 lessons in Indices and Logarithms

  1. 1Reading Repeated Factors as IndicesExpress numbers in index form
  2. 2Index Forms with a Specified BaseExpress numbers in index form
  3. 3Discovering Product and Quotient LawsDerive the laws of indices using factors
  4. 4Power of a Power and Identity CasesDerive the laws of indices using factors
  5. 5Indices in Measurement and DesignApply the laws of indices in different situations
  6. 6From Powers of Ten to Common LogsRelate index notation to logarithm notation to base 10
  7. 7Interpreting Base-Ten LogarithmsRelate index notation to logarithm notation to base 10
  8. 8Reading Common Logarithms in TablesDetermine common logarithms of numbers from mathematical tables and calculators
  9. 9Comparing Table and Calculator LogarithmsDetermine common logarithms of numbers from mathematical tables and calculators
  10. 10Logarithms for Multiplication and DivisionApply common logarithms in multiplication, division, powers and roots of numbers
  11. 11Logarithms for Powers and RootsApply common logarithms in multiplication, division, powers and roots of numbers
  12. 12Integrated Logarithmic ComputationApply common logarithms in multiplication, division, powers and roots of numbers
  13. 13Why Indices and Logarithms MatterAppreciate the use of indices and common logarithms in mathematical computations