LESSON: Rounding Decimals

READ: Round Very Small Decimals

Round Very Small Decimal Fractions to the Leading Digit

We know that a decimal is a part of a whole. We also know that some decimals are smaller than others. If we have a decimal that is 5 tenths of a whole, this is a larger decimal than 5 hundredths of a whole. Let’s look at those two decimals.

Example

.5 ______ .05

If we were going to compare these two decimals, we would add a zero to the first decimal so that it has the same number of digits as the second.

.50 > .05

We can see that the five tenths is greater than five hundredths. This example can help us to determine very small decimals.

A decimal is a very small decimal depending on the number of places represented after the decimal point. The more decimal places, the smaller the decimal is.

Here is an example of a very small decimal:

.000056787

Because this decimal has so many digits, we can say that it is a very tiny decimal. We can round tiny decimals like this one too. We use something called the leading digit to round a very small decimal. The leading digit is the first digit of the decimal that is represented by a number not by a zero.

In this example, the leading digit is a five:

.000056787

To round this decimal, we use the leading decimal and add in the rounding rules that we have already learned. The digit to the right of the five is a six. Six is greater than 5, so we round up.

Our answer is .00006.

Notice that we include the zeros to the left of the leading digit, but we don’t need to include any of the digits after the leading digit. That is because we rounded that digit so we only need to include the rounded part of the number.