What is Place Value? - Definition & Examples

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  • 0:00 Money And Place Value
  • 0:59 Further Exploring Place Value
  • 4:00 Steps To Finding The…
  • 5:14 Lesson Summary
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Lesson Transcript
Instructor: Laura Pennington

Laura received her Master's degree in Pure Mathematics from Michigan State University. She has 15 years of experience teaching collegiate mathematics at various institutions.

Every digit in a number has a place value. In this lesson, through definition and example, we will learn what a place value is and how to find the place value of a specific digit. At the end of the lesson, you can continue practicing with a quiz.

Money and Place Value

Whether we have it or not, we are all very familiar with money and how to write different amounts of money. Consider the amount $154.37. We know these numbers preceded by the dollar sign represents one hundred fifty-four dollars and thirty-seven cents, but have you ever thought about what each of the digit's values are in a given amount of money? For example, the 5 in $154.37 isn't just worth five pennies. Its location is two units to the left of the decimal point, so in terms of money, the 5 is worth fifty dollars. Similarly, the 1 is worth one hundred dollars, the 4 is worth four dollars, the 3 is worth thirty cents, and the 7 is worth seven cents. We see that the value of the digit depends on its location in the number. In mathematics, we call this a place value, and it applies to all numbers, not just money.

Further Exploring Place Value

The place value is the value of the location of a digit in a number. The place values are determined by how many places the digit lies to the right or the left of the decimal point.

The place values to the left of the decimal point are increasing powers of 10:

  • The first place to the left of the decimal point is the ones place, or 10^0.
  • The second place to the left of the decimal is the tens place, or 10^1.
  • The third place to the left of the decimal is the hundreds place, or 10^2.

The pattern continues. In general, the nth place to the left of the decimal has place value 10^(n - 1). For example, consider the number 136,774.8591. The digit 3 in this number falls five places to the left of the decimal. This place is determined by 10^(5-1) = 10^4 = 10,000, so this is the ten-thousands place. Therefore, the 3 in 136,774.8591 has place value 3 * 10,000 = 30,000.

The place values to the right of the decimal are decreasing in powers of 10:

  • The first place to the right of the decimal is the tenths place, or 10^-1.
  • The second place to the right of the decimal is the hundredths place, or 10^-2.
  • The third place to the right of the decimal is the thousandths place, or 10^-3, and so on.

In general, the nth place to the right of the decimal has place value 10^-n. For example, in our number 136,774.8591, the 9 falls three places to the right of the decimal, so it falls in the 10^-3 = 1 / 1000 place, or in the thousandths place. Therefore its place value is 9 / 1000, or nine-thousandths.

The following image illustrates the different place values of a number:

Place value chart
Place Value 2

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