Base 10: decimal numbers

• Base 10: decimal numbers


  A system of counting and arithmetic that relies on having ten different symbols for digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
• Counting up in base 10


  When you arrive at 9, the next number is represented by placing a 1 one place to the left and a 0 to the right, giving 10
• Base 10 numbering system

  • The 1 represents the number of tens
  • Each column has ten times the value of the column to its right
  • Can extend the system indefinitely by adding columns to the left (hundreds, thousands, ten thousands, etc.)
• Columns in base 10 numbering system

  • Ten thousands
  • Thousands
  • Hundreds
  • Tens
  • Units
• Weighting


  The value of each column, found by multiplying the weighting to the right by 10
• The first weighting (on the far right-hand side) is 1
• Base 10 numbering system

  Also called a decimal numbering system
• Place value systems


  • Numbering systems that use a set of digits or symbols and weighted columns
  • Not all numbering systems are place value systems (e.g. Roman numerals)
• Arithmetic is very difficult in non-place value systems like Roman numerals