# 3.13: Small Decimal Rounding to a Leading Digit

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

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

Have you ever studied money from other countries?

Well one day while Julie and Jose were waiting for customers, they began trying to figure out how much a Mexican Peso was worth in US money. Jose was reading a book on different currencies and this is how the whole conversation began.

Julie looked up the exchange rate on the internet and discovered the following fact.

On the day that she checked, .074 US dollars was equal to 1 Peso.

In the last few Concepts, you have been learning how to round decimals. You have used a number line and place value to round. Now you are going to learn how to round using leading digits.

**Pay attention and you will be able to round this value to the leading digit.**

### Guidance

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.

.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.**

.000056787

**Wow! That is a lot of digits. 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 zero. In this example, the leading digit is a five.

.000056787

To round this decimal, we use the leading digit 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.*

**It is your turn to apply this information, round each small decimal by using the leading digit.**

#### Example A

**.0004567**

**Solution: .0005**

#### Example B

**.0000178923**

**Solution: .00002**

#### Example C

**.00090034**

**Solution: .0009**

Do you know how to round the currency from the opening dilemma? Here it is once again.

Well one day while Julie and Jose were waiting for customers, they began trying to figure out how much a Mexican Peso was worth in US money. Jose was reading a book on different currencies and this is how the whole conversation began.

Julie looked up the exchange rate on the internet and discovered the following fact.

On the day that she checked, .074 US dollars was equal to 1 Peso.

Using leading digits, we can round this value.

The first digit that we see is a 7, but the value following it is a 4. Since four is less than five, we don't round the seven up. It stays the same.

**\begin{align*}.07\end{align*} .07 is our answer.**

### Vocabulary

Here are the vocabulary words found in this Concept.

- Round
- to use place value to change a number whether it is less than or greater than the digit in the number

- Decimal
- a part of a whole written to the right of a decimal point. The place value of decimals is marked by THS (such as tenTHS, hundredTHS, etc).

- Leading Digit
- the first digit of a tiny decimal that is not a zero

- Small decimals
- decimals that have several zeros to the right of the decimal point before reaching a number.

### Guided Practice

Here is one for you to try on your own.

On August 5, 2007, the Japanese yen was worth .008467 compared to the US dollar.

Round using leading digits.

**Answer**

First, let’s find the leading digit. The first digit represented by a number not a zero is 8. Now we apply our rounding rules. The digit to the right of the 8 is a 4. So the 8 remains the same.

**Our answer is .008**

### Video Review

Here are videos for review.

James Sousa, Rounding Decimals

Khan Academy Rounding Decimals

### Practice

Directions: 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

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

Here you'll learn how to round very small decimal fractions to the leading digit.

## Concept Nodes:

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.