If a decimal has an extra zero at the end, we can remove this extra zero without changing the number.

For example, to find a decimal that's the same as we simply remove the zero at the end:

Because and represent the same decimal number, we say that they are equivalent decimals.

Why does this work? Let's look at the place value chart for

We can see that there is a zero in the hundredths column, and there are no smaller place values (for example, there are no thousandths). So, we can remove the hundredths column:

We're not restricted to removing just one zero to make an equivalent decimal.

For example, to make a decimal that's equivalent to we can remove the block of two zeros at the end:

Similarly, we can make a decimal that's equivalent to by removing the block of three zeros:

Note that after we remove the block of three zeros, there are no more numbers after the decimal place, so we can remove the decimal place as well.

When we attach an extra zero on the right of a decimal, its value stays the same.

For example, and represent the same number:

Once again, we say that is equivalent to

We're not restricted to just one zero. We can attach as many as we'd like! For example, the numbers

are both equivalent to They're also equivalent to each other!

We can also find decimals that are equivalent to whole numbers. Let's see an example.