Learning About Metric Measures (1970)

[Music] For his school project, Jim is preparing to construct a scale model of the Earth. the sun and the distance between. The sizes and distances are shown on this chart. The diameter of the Earth is about 8,000 mi. The diameter of the sun is about 864,000 mi and the distance between them is about 93 million miles. Jim had planned to use a scale in which 1/8 in represents 1,000 miles. But Jim has become so discouraged trying to convert distances like 93 million miles into the scales 8 in units that he's about ready to give up the whole project. Then Jim's father makes a suggestion. Instead of using a common ruler with its clumsy 8 in, inches and feet, why not use this meter stick that he uses in his engineering work? It too is a kind of measuring ruler. Jim's father also shows Jim where to find more information about the meter stick. Jim learns that the meter is the basic unit of length in a system of measurement called the metric system. The meter stick itself represents the length of 1 meter, which is about a yard. Since Jim has decided to do his measuring with the meter stick, he wants to make a model of it to learn how it works. So he cuts a strip of cardboard 1 meter in length. Jim labels the cardboard strip with the word meter followed by its abbreviation M. Jim notices that the meter stick is divided into several smaller units. There are very tiny units. There are larger numbered units and there are units that are still larger. How do the sizes of these various units compare? To find out, Jim counts the largest of the units. One 2 3 4 5 6 7 8 9 10. There are 10. Because there are 10 of these larger units in a meter, we can think of each of them as 1/10enth of a meter. The word we use for 1/10enth of a meter is decimeter. After he has marked the cardboard strip into decimeters, Jim labels one of the units decimeter and writes its abbreviation DM. As we have seen, each decimeter is also divided into smaller units. The numerals labeling these units tell us that there are 10 of the smaller units in a decimeter. How many do you think there are in a meter? Since there are 10 of the smaller units in a decimeter and there are 10 decimeters in a meter, there should be 10 * 10 or 100 of these smaller units in a meter. Jim counts them in groups of 10 to see. 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. Since there are 100 of these smaller units in a meter, each is 1/100th of a meter. The word for 1/100th of a meter is centimeter. Each centimeter on the meter stick has in turn been divided into still smaller units. How many of these smaller units do you think are in a centimeter? We have seen that there are 10 decimeters in a meter. We have also seen that there are 10 cm in a decimeter. This makes a pattern of 10 to 1. Using the pattern 10 to 1, we can predict that there should be 10 of these very small units in a centimeter. Count them and see. There are 10 in a centimeter. The pattern 10 to 1 works. Jim divides one of the centimeters on the cardboard strip into 10 of the very small units. If a centimeter contains 10 of these very small units, how many does a decimeter contain? Since there are 10 cm in a decimeter, there should be 10 * 10 or 100 of these very small units in a decimeter. Let's count them in groups of 10 on the meter stick and see. 10, 20, 80, 90, 100. If there are 100 of these very small units in a decimeter, how many should there be in a whole meter? How many did we find are in a centimeter? 10. How many centimeters are there in a decimeter? 10. And how many decimeters are there in a meter? 10. Do you see that? This makes a pattern of 10 * 10 * 10 or 1,000. Let's count the very small units in groups of 100, 100, 200. 800, 900, 1000, or 1,000. Since each of these very small units is 1 1,000th of a meter, each is called a millimeter, a word meaning 1 1,000th of a meter. Jim now makes a chart that shows the relationship between the decimeters, centime, and millime on the meter stick. The chart shows that 1 meter is equivalent to 10 decimeters. 1 decimeter is equivalent to 10 cm and 1 cm is equivalent to 10 mm. To put it another way, 1 meter is equivalent to 10 decimeters or to 100 cm or to 1,000 mm. Since he is using the meter stick to build his model of the earth and the sun, Jim has made a new scale in which 1 mm represents 1,000 miles. According to this new scale, the diameter of the model Earth is to be 8 mm since the real Earth is about 8,000 mi in diameter. The diameter of the sun is to be 864 mm and the distance between the earth and the sun is to be 93,000 mm or 93 m. To help him find a sphere of the right size to represent the Earth, Jim sets the tips of his calipers so that they are 8 mm apart. After Jim has found a sphere of the right size to represent the Earth, he looks for the point on the meter stick that represents the size of the model sun, which is to be 864 mm. Jim has found out that the measure 864 mm can also be thought of as 8 decime plus 6 cm plus 4 mm. Just as the number 864 can be thought of as 800s plus 6 10 plus 4 1's. This is because the metric system works just like our decimal system of numeration by which we write numbers. Jim now blows up the balloon that is to represent the 864,000mi diameter of the sun. When he has finished, Jim checks the size of the balloon on the meter stick to make sure it is 864 mm in diameter. By comparison with the sun, the 8 mm Earth model, which represents the 8,000mi diameter of the Earth, is very small indeed. Jim now drives a stake and fastens the Earth model to it. He measures off the 93 m which represent the 93 million miles that separate the earth from the sun. When he has finished measuring, Jim fastens the balloon which represents the sun to another stake and the model is complete. By using metric units for his scale, Jim was able to represent distances like 93 million miles very easily. Why do you think Jim found it easier to use metric units to represent these distances than it was to use 8 in, inches, and feet? [Music]