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PCAT: Study Guide & Test Prep62 chapters | 651 lessons | 53 flashcard sets

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Zero is a very small but also very important digit. Watch this lesson and learn how it is used in decimal numbers to keep place and for accuracy purposes.

**Decimal numbers**, those numbers with a decimal point, are all around us. Just go shopping and you will see them everywhere. Your favorite pair of shoes probably cost you a decimal number, such as $29.99 or even $89.95 for an expensive pair. Notice the decimal point in both cases.

Step over into the big electronics section of the store and look at how much the large screen televisions cost. You might see a price tag of $1,099.95 for a really large television. Do you see the zero in that price? What is that zero telling you?

That zero in that number is acting as a placeholder. It is telling you that the hundreds place is a zero, and the one to the left of it is for the thousands place. If we wrote the number without the zero, what would we have? We would have $199.95.

If we saw that kind of price tag for a really large television, we would think that somebody must have made a mistake, or it's a really good deal and we should definitely buy it right away. That number without the zero, the $199.95, just brought down the price of the large screen TV by $1,000! That's a lot of money that's missed!

Zeros that you see before a number are called **leading zeros**. When you see leading zeros to the left of a whole number, such as 0045, they can be ignored. The zeros are simply telling you that this particular number has no larger values. 0045 is the same as 45. The zeros don't give you any additional information that you need, so you can ignore them, and we do in math. Instead of writing 0045, we write 45.

However, if the leading zeros are in a decimal number, such as .0045, then we have to keep them. In this case, they are acting as placeholders. The zeros in front of the 45 but after the decimal point tell you how small this number is. .0045 is not the same as .045 or .45. They are all different numbers. .0045 is smaller than .045, and .045 is smaller than .45. So remember, if you see a decimal point, then any leading zeros after that have to stay because they tell you how small your decimal is.

**Trailing zeros**, the zeros at the end of a number, can be ignored if you see them in a decimal number. For example, the trailing zeros in the decimal number .004500, the zeros after the five, can be ignored because they don't give you any additional information. They just tell you that your value ends with the last digit. Trailing zeros in decimal numbers are like leading zeros in whole numbers.

Trailing zeros in whole numbers, though, are the opposite. You have to keep them because now they tell you how big your number is. For example, 4,500 is different than 450 and 45. 4,500 is larger than 450, and 450 is larger than 45.

The only time where you would keep your trailing zeros after a decimal number is when you want to show accuracy. For example, when you are shopping, you want to see two decimal numbers so you know how much you are paying. It would be weird to look at a price tag that only shows $4.5 instead of $4.50. This trailing zero is there to show you that this decimal is accurate to two decimal places.

Let's review what we've learned now. We've learned that **decimal numbers** are the numbers with decimal points in them. **Leading zeros** are the zeros in front of a number, and **trailing zeros** are the zeros after a number.

You can think of trailing and leading zeros as switching roles on either side of the decimal point. Trailing zeros can be ignored to the right or after a decimal point, and leading zeros can be ignored if they are in front of or to the left of a decimal point. Trailing zeros before a decimal point and leading zeros after a decimal point have to stay because they tell you how big or small your number is. The only time that trailing zeros are kept in a decimal number is when you want to show accuracy.

Once you have completed this lesson, you should be able to:

- State the purposes for leading and trailing zeros
- Explain when you should and should not keep trailing and leading zeros

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PCAT: Study Guide & Test Prep62 chapters | 651 lessons | 53 flashcard sets

- Go to Gas Laws

- What is a Decimal Place Value? 6:19
- Comparing and Ordering Decimals 8:56
- How Zeros Are Used in Decimals 6:39
- Adding and Subtracting Decimals: Examples & Word Problems 6:53
- Multiplying and Dividing Decimals: Examples & Word Problems 5:29
- How to Estimate with Decimals to Solve Math Problems 8:51
- Go to Decimals

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