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Transcript: Place Values After the Decimal Point
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BYU-Idaho Online Learning

Video Transcript

Place Values After the Decimal Point

[One speaker] 

[Any necessary descriptions.]

Narrator: Welcome to the video on place values after the decimal point. So what is a decimal point? [a number is shown on the screen: 6,781,239,465. The decimal point is highlighted in red.] A decimal point is the little point that you see right here after the whole number, and any numbers to the right of the decimal point show a portion of a whole number. So once we’re into the numbers on the right of the decimal point we’re no longer talking about the whole thing, we’re talking about a portion of it.

The farther that we go to the right, the smaller that portion becomes. For example, if we have point seven, this seven represents tenths. So this seven represents seven tenths. Remember when we had the number one thousand four hundred and eighty-three? We described it visually by having one set of one thousand, which is ten one hundreds, four sets of one hundred, eight groups of ten, and three ones. Decimals express numbers that are even smaller than our little one.[different blue blocks are shown on the screen.] Let’s look at point seven. Let’s show what this means by zooming in on our little blocks. In this picture we zoomed in on one little block. Notice it can be divided up into additional blocks. This block has been divided into ten parts.

Point seven represents having seven of those ten little parts. The next place value after the tenths is the hundredths. The hundredths represent an even smaller breakdown of our one unit. Here we are at our little point seven unit. We can zoom in even more and see an even smaller breakdown. Now we’ve zoomed in even closer on our point seven. Now we see the block is divided up into one hundred little segments, and we have seventy of those segments.

Point seven two represents having seventy-two of these little blocks. So point seven two, or seventy-two hundredths, represents seventy-two out of one hundred pieces of one little block, that’s why the two is in the hundredths place value.  If we zoomed in again we could see our same block divided into a thousand pieces. The next place value represents the thousandths place value. We can then see a box divided into a thousand pieces, and each one of those little pieces would represent one out of a thousand of those little tiny pieces of the big block. After the thousandths comes the ten thousandths place. Again, if we took that same block and we zoomed in even closer and we divided it up into ten thousand little segments. So in this case, we would have seven thousand two hundred forty pieces of the block broken into ten thousand little segments. The next place value is the hundred thousandths.

Notice these names mirror the names on the left hand side, but recognize that these are small, each time that we go one more place value to the right the little segments get smaller and smaller. Whereas on the left hand side, with every place value the next one gets ten times bigger. Similarly, each time we go another place value to the right the numbers get ten times smaller. These numbers can keep going on and on as far as we can go.

Each of the place values has the name, but just for our sake we’re not going to go beyond the millionths. Now, how do you actually say this number? We don’t generally use these names, we use these names when we’re talking about rounding to a specific place value, which we’ll talk about in a future lesson, but generally when we say a number with a decimal point we say six billion seven hundred eighty-one million two hundred thirty-nine thousand four hundred sixty-five points, for the decimal point, seven two four zero six nine. [6,781,239,465.72409]

So in general, when we talk about decimals in this class, we will simply say point and then say the numbers in order after the decimal point. Another way to say numbers that have decimals in them is to say the number and then give the last place value.

For example, five point seven could be said five and seven tenths because the last number to the right in this number is in the tenths place. Another example would be five point seven three, in this case we can say five and seventy-three hundredths.

Notice I said and between the two, and represents the decimal point. Sometimes people say and between place values greater than the ones. For example, four hundred sixty-five, not four hundred and sixty-five because the proper way to say it is and represents the decimal.

So in this case five and seventy-three hundredths. Or, to give one more example, five and seven hundred thirty-two thousandths. Meaning out of a thousand little pieces we have seven hundred and thirty-two.

Notice, I already made the mistake in my natural speech in adding the word ‘and’ in a place that didn’t represent the decimal point. So you can’t always rely on the word ‘and’ to mean the decimal point. And this is also why it’s a little bit more clear to use ‘point’ when talking about a decimal point.  

[End of Video]