Place values are an essential concept in understanding how numbers are written and represented. They determine the significance and position of each digit within a number. The value of a digit depends on its place or position within the number, and this value changes as you move left or right.
1. To the left: As you move to the left, each place value position is ten times greater than the previous position. For example:
- 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, when you move to the left, the place values increase by a factor of 10.
2. To the right: As you move to the right, each place value position is ten times smaller than the previous position. This is known as a decimal fraction or a fraction of a whole number. For example:
- 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.
So, when you move to the right, the place values decrease by a factor of 10.
Understanding the relationship between place values helps in reading and writing numbers accurately. It allows us to identify the value of each digit and determine the overall value of a number.