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Working with Decimals

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  • 1:09 How to Read & Write Decimals
  • 2:31 What Do the Zeroes Do?
  • 3:48 Which One Is Bigger?
  • 5:14 Rounding Decimals
  • 6:30 Scientific Notation
  • 8:08 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.

After watching this video lesson, you will become well acquainted with decimals and how to work with them. Learn how you can use them to help you describe what is going on around you.

Decimals

In this video lesson, we'll cover decimals and what decimals can do for you. Decimal numbers are the mathematical numbers that have a decimal point in them. You will find scientists, mathematicians, fashion designers, and chefs - to name a few - using these types of numbers to help them describe amounts that are not whole numbers.

For example, a chef may need to add 0.25 teaspoons of baking powder to his bread dough. One teaspoon would be too much and would ruin his bread. By using a decimal number, it gives the chef the precision he needs to make deliciously yummy bread. Fashion designers likewise need to be exact in their measurements when cutting fabrics to make their new designs. For example, they may need exactly 1.125 yards of royal blue satin fabric to make their latest dress. If they were given only one yard, it wouldn't be enough. If they cut too much, the dress would look out of shape because too much fabric is used. As you can see, decimals are used in important ways in the real world.

How to Read & Write Decimals

Reading decimals is a pretty straightforward matter. You actually just read it as you see it. You first say the number in front of the decimal, just like you would a regular number, then you say point when you see the decimal point, and then you finish by reading the digits one by one that follow. So, for example, 0.25 teaspoons is read as zero point two five teaspoons. 1.125 yards is read as one point one two five yards.

How would you read a decimal such as 0.0034? Did you say zero point zero zero three four? If you did, then you are correct! What about 34.12? Did you say thirty-four point one two? Then you are right again!

Writing decimals is pretty straightforward too. You write them as you hear it. If you heard a scientist on TV say fifty point three, then you would first write down 50, then a dot for the decimal point, and then finally a 3 following the decimal point. You end up with 50.3 for your number. What if you heard one hundred one point five four? What would you write? If you wrote down 101.54, then you are right on the ball!

What Do the Zeroes Do?

Did you notice the number 0.0034 has a bunch of zeroes before we see any non-zero digits? These zeroes actually play a very important role. The zeroes after the decimal point and before our first non-zero digit tell us just how big or small our decimal is. It's just like zeroes for our regular numbers. For example, 100 is bigger than 10 because it has more zeroes. In decimals, 2.01 is bigger than 2.001.

When we deal with numbers to the right of the decimal point, they work in the opposite way than numbers to the left of the decimal point. 10 and 100 are numbers to the left of the decimal point, and when you have more zeroes on this side of the decimal point, they make our numbers bigger. To the right of the decimal point, the more zeroes in the beginning you have, the smaller the number. That's why 0.01 is bigger than 0.001. The 0.001 has more zeroes than 0.01, and both are numbers to the right of the decimal point.

Which One Is Bigger?

Knowing that numbers work differently to the right of the decimal point than they do to the left of the decimal point will help you compare your decimal numbers. You know that 20 is bigger than 10. If you saw the decimal numbers 0.01 and 0.02, which one would you think is bigger? The 0.02 is bigger because we are comparing the digits in the same location. Both the 1 and the 2 are two spaces to the right of the decimal point. Because they both have one zero in front of them, we need to compare the digits themselves.

But if we were comparing 0.01 and 0.002, we wouldn't need to compare the digits because they are in different locations. One number has more zeroes in front than the other. This tells you that the number with more zeroes in front is smaller. So, 0.01 is bigger than 0.002. Now you try comparing 0.34 and 2.12. Which one is bigger and which is smaller? For this one, you see that to the left of the decimal number, one is 0 and the other 2. Just from this information alone, you already know which number is larger and which is smaller. The 2.12 is bigger and the 0.34 is smaller.

Rounding Decimals

Sometimes, you will see a decimal number that is super long that you will need to round just so you can write it down on paper, and so you can work with it in calculations without it being too cumbersome. For example, you might come across a decimal like 3.141592653589793238462643383279502884197169399375105820974944592307816406286.What do you do? Do you write this number out each time you work with it? No! What you do is determine how much accuracy you need.

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