Describe how the different place values in base ten are related?

Question

Describe how the different place values in base ten are related. Namely how are ones, tens, hundreds, thousands etc. related to each other. Also, explain the relationship among smaller place values such as tenths, hundredths, thousandths and ten-thousandths.

Answer 1

As you move to the left, each place is 10 of the place before.

10 is ten ones.

100 is ten tens.

1000 is 10 hundreds.

Etc.

Going the other way, to the right, the opposite is true.

One is 1/10 of 10.

The same goes on the right of the decimal, where the places are < 1.

1 is ten tenths.

0.1 is 10 hundredths.

Etc.

Going right, each place is 1/10 of the place before it.

If 10 is ten ones, then 1 is 1/10 of 10.

0.1 is 1/10 of 1.

0.01 is 1/10 of 0.1.

Etc.

Answer 2

David's answer is correct and thorough. I am not sure what age or grade level I am targeting. I do know that by 4th grade, students are expected to see the relationship between place value categories as a "10 times as many" phrase.

For example: a digit in the ten's place is 10 times as much as that same digit in the one's place.

a digit in the thousand's place is 10 times as much as that same digit in the hundred's place.

By 5th grade, students are expected to see the relationship going in the reverse. For example: a digit in the hundred's place is one tenth as much as that same digit in the ten's place.

This is a very important concept that is developed gradually during the elementary school years that allows students to make sense of solving equations including all 4 operations with whole numbers, fractions, and decimal fractions.