# How Zeros Are Used in Decimals

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• 0:01 Decimal Numbers
• 3:48 Trailing Zeros
• 4:55 When to Use Them
• 5:32 Lesson Summary
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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

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.

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