Place Value

Understanding the place value for numbers is vital, as it ensures the student can write the number down correctly. The place value denotes which number is going to be placed in which position and how much of a value it has. It also allows a person to read a number and know how large it is. With more advanced math problems, it can be crucial in determining decimal points when numbers are multiplied.

Determining the Place Value for Whole Numbers

The number system is based on 10 numbers, 0 to 9. When these are written alone, they’re in the ones position. If two numbers are put together, the first one, on the left, is in the tens position and the second one is in the ones position. So, for 72, 7 would be in the tens position and 2 would be in the ones position.

Further positions include hundreds, thousands, ten thousands, one hundred thousands, millions, and so on. The number 20,306 would have a 2 in the ten thousands position, a 3 in the hundreds position, and a 6 in the ones position.

Determining the Place Value for Decimals

In determining the place value for whole numbers, the ones are the furthest right and the place value goes up to the left so the tens are to the left of the ones. In determining the place value for decimals, the place value goes the opposite way, starting with the tenths. Reading to the right of the decimal are the tenths, hundredths, thousandths, ten thousandths, and so on.

For example, the number 0.938 has a 9 in the tenths position, a 3 in the hundredths position and an 8 in the thousandths position. The number 4.2 would have a 4 in the ones position and a 2 in the tenths position.

This can be helpful in determining fractions as well. For 6.3, the number 3 is in the tenths position and, as such, would be equal to 3/10. The number can be written as 6.3 or 6 3/10. With 0.81, the 8 is in the tenths position and the 1 is in the hundredths position, so the fraction equivalent would be 81/100.

Using a Chart to Determine Place Value

Learning to determine the place value of numbers can be difficult, but using a place value chart can make this easier. The chart reads from left to right starting with what the largest place value might be and goes to what the smallest might be. For whole numbers, it might go from the millions position to the ones position and with decimals it might go to the thousandths position. These are written at the top of the charge and the student can fill in the chart with their numbers to make it easier to see which place value each number has.

Try using the place value chart now to determine the place value for a variety of numbers, both whole numbers and decimals. This will help you ensure you understand how to determine the place value and how to write numbers when you need to do more advanced math problems like moving the decimal over one or more place values.