Place values are a fundamental concept in understanding numbers. They help us determine the worth or significance of each digit within a number. The value of a digit depends on its position or place within the number, and this value changes as you move left or right.
1. Moving to the left: When you move to the left, each place value position is ten times greater than the one before it. Let's look at some examples:
- In the number 10, the digit 1 is in the "tens" place. Its value is 1 * 10 = 10.
- In the number 100, the digit 1 is in the "hundreds" place. Its value is 1 * 100 = 100.
So, as you move to the left, the place values increase by a factor of 10.
2. Moving to the right: When you move to the right, each place value position is ten times smaller than the one before it. This is referred to as a decimal fraction or a fraction of a whole number. Consider these examples:
- In the number 0.1, the digit 1 is in the "tenths" place. Its value is 1 * 0.1 = 0.1.
- In the number 0.01, the digit 1 is in the "hundredths" place. Its value is 1 * 0.01 = 0.01.
Thus, moving to the right, the place values decrease by a factor of 10.
Understanding place values is crucial for accurately reading and writing numbers. It enables us to determine the value of each digit and calculate the total value of a number.