1.1.5 Order By Size

What is place value?

• Place value refers to what digits within a number represent
  • E.g. in the number 327.5
    • 3 represents 300 (3 hundreds)
    • 2 represents 20 (2 tens)
    • 7 represents 7 (7 ones)
    • 5 represents 0.5 (5 tenths)
• Place value helps you to see the size of a number
• Place value can be used to order numbers
• Standard form can be used with place value

Ten thousands	Thousands	Hundreds	Tens	Ones (units)	Decimal point	Tenths	Hundredths
10 000	1 000	100	10	1	.	0.1 or	0.01 or
104	103	102	101	100	.	10-1	10-2

Putting numbers into order – isn’t this easy?

• Yes! Until the numbers start including a mixture of fractions, decimals and/or percentages
• There could also be numbers written as powers/indices and (square/cube) roots included too
• Then there is the use of mathematical inequality symbols too:
  • ≠ not equal to
  • < less than
  • ≤ less than or equal to
  • > greater than
  • ≥ greater than or equal to

• To arrange numbers in order they all need to be written in the same format
• Usually, decimals are the easiest to compare
• Before continuing make sure you can convert:
  • fractions to decimals
  • percentages to decimals

• Also make sure you can evaluate ...
  • powers/indices (eg 4² = 4 x 4 = 16)
  • common square roots and cube roots (eg √ 4 = 2)

• For more awkward cases you may need to use a calculator

How do I put decimals in order?

• The easiest way is to compare the numbers digit by digit
  • Write the numbers one underneath the other, in neat, lined up columns
  • Reveal each number one digit at a time, from the left
    (ie highest place value first)
  • Make a note of the order as you go

Summary

• STEP 1  Convert all values to decimals
• STEP 2  Write as a neat column with digits lined up
• STEP 3  Reveal one digit at a time and order them when possible
• STEP 4  Write decimals in order
• STEP 5  Write final answer using numbers in their original format