Place Value

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The value of a digit depends on its place value: its position in the number. On an exam, you may be asked to identify the name of a place value or the value of a digit in a particular place value. Place values decrease in value from left to right. For example, a 7 in the hundreds place indicates “seven hundred,” while a 7 in the tens place only indicates “seventy.” There are place values on both sides of the decimal point. To begin with, let's name the place values to the left. Take the number 9,876,543,210. The place values in this number are as follows:
  • 9: billions
  • 8: hundred millions
  • 7: ten millions
  • 6: millions
  • 5: hundred thousands
  • 4: ten thousands
  • 3: thousands
  • 2: hundreds
  • 1: tens
  • 0: ones
Notice how the place values increase by a power of ten as they move away from the decimal point: 1 x 10 = 10, 10 x 10 = 100, 100 x 10 = 1000, and so on. Also, notice how each group of three digits, beginning with the ones place and moving left, is separated by commas. These groups of three digits are called periods. The place values to the right of the decimal point are quite similar. Consider the number 0.123456789:
  • 0: ones
  • 1: tenths
  • 2: hundredths
  • 3: thousandths
  • 4: ten-thousandths
  • 5: hundred-thousandths
  • 6: millionths
  • 7: ten millionths
  • 8: hundred millionths
  • 9: billionths
Note that the first place value to the right of the decimal point is the tenths place: there is no such thing as a "oneths" place.