# 3.13: Small Decimal Rounding to a Leading Digit

**At Grade**Created by: CK-12

**Practice**Small Decimal Rounding to a Leading Digit

Donte enjoys learning about different currencies and how the currencies have changed in value over time. He learns that on August 5, 2007, the Japanese yen was worth 0.008467 compared to the US dollar. He wants to round the decimal, but he isn't sure how to do it. How can Donte round 0.00847?

In this concept, you will learn how to round very small decimals to the leading digit.

### Rounding Decimal Values to the Leading Digit

A **very small decimal** is determined by the number of places represented after the decimal point. The more decimal places, the smaller the decimal is.

Let's look at an example.

0.000056787

This decimal is a very small decimal.

You can round tiny decimals like this one using something called the **leading digit**. The leading digit is the first digit of the decimal that is represented by a number other than zero. In this example, the leading digit is a five.

0.000056787

To round this decimal, start with the leading digit then check the digit to the right of the leading digit. The digit to the right of the five is a six. Six is greater than 5, so round up.

The answer is 0.00006.

Include the zeros to the left of the leading digit, but you don’t need to include any of the digits after the leading digit.

### Examples

#### Example 1

Earlier, you were given a problem about Donte and the value of yen on August 5, 2007. The yen was worth 0.008467 compared to one U.S. dollar. What is 0.008467 rounded to the leading digit?

First, identify the leading digit.

8

Next, determine if the number to the right of the leading digit is 5 or greater.

No

Then, round the leading digit the same.

0.0008

The answer is 0.0008.

#### Example 2

Round 0.000086002

First, identify the leading digit.

8

Next, determine if the number to the right of the leading digit is 5 or greater.

Yes

Then, round the leading digit up.

0.00009

The answer is 0.0009.

#### Example 3

Round 0.0004567 to the leading value.

First, identify the leading digit.

4

Next, determine if the number to the right of the leading digit is 5 or greater.

Yes

Then, round the leading digit up.

0.0005

The answer is 0.005.

#### Example 4

Round 0.0000168923 to the leading value.

First, identify the leading digit.

1

Next, determine if the number to the right of the leading digit is 5 or greater.

Yes

Then, round the leading digit up.

0.00002

The answer is 0.00002.

#### Example 5

Round 0.00090034 to the leading digit.

First, identify the leading digit.

9

Next, determine if the number to the right of the leading digit is 5 or greater.

No

Then, keep the leading digit the same.

0.0009

The answer is 0.0009.

### Review

Round each to the leading digit.

1. .0045

2. .0067

3. .000546

4. .000231

5. .000678

6. .000025

7. .000039

8. .000054

9. .0000278

10. .0000549

11. .00060789

12. .00045612

13. .00390087

14. .000003812

15. .00090871

### Review (Answers)

To see the Review answers, open this PDF file and look for section 3.13.

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Decimal

In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).Leading Digit

The leading digit of a decimal number less than one is the first digit to the right of the decimal point that is not a zero.Round

To round is to reduce the number of non-zero digits in a number while keeping the overall value of the number similar.Small decimals

Small decimals are decimal numbers that have several zeros to the right of the decimal point before reaching a non-zero number.### Image Attributions

In this concept, you will learn how to round very small decimals to the leading digit.