The Number System

What is place value?

• When a number is written down using digits, each digit has a value depending on where it is within the number
• For example for the number 9876
  • The 6 represents 6 ones (or units)
  • The 7 represents 7 tens
  • The 8 represents 8 hundreds
  • The 9 represents 9 thousands
• In words, this number is nine thousand, eight hundred, and seventy six

How do I read large numbers?

• Each place has a value ten times larger than the place to the right of it
• For example for the number 12345678

• When dealing with large numbers, it is often helpful to write them with a space between some of the digits
  • We do this after every 3 digits from the right
  • For example, 12345678 could be written as 12 345 678
• This number would be twelve million, three hundred and forty five thousand, six hundred and seventy eight

How does place value work for decimals?

• Each place has a value ten times larger than the place to the right of it
• This means for decimals, the decimal places further to the right are worth less
• Lets look at the number 23.45678
  • We would read this as twenty three point four five six seven eight
  • However, each place has a different value

• The 4 represents 4 tenths, or 0.4
• The 6 represents 6 thousandths, or 0.006
• You will often hear these place values used relating to time
  • For example in a sprint race, athletes may be separated by "5 hundredths of a second" or 0.05 seconds