4th Grade - Math

LESSON PROBLEM: Measurement: If you are asked to convert a distance from hectometers to centimeters, how would you go about it?


STUDY GUIDE

When we think of places, we think of distance. When you are asked to go to a store to buy rice, you think of the distance. Your mode of transportation depends on the distance you have to cover. If it is close by, you might walk; if it is somewhat farther, you may decide to go by bike.

One basic unit of distance is the meter. The units that we use to measure or refer to distance are in the metric system:

1.Kilometer
2.Hectometer
3.Decameter
4.Meter
5.Decimeter
6.Centimeter
7.Millimeter

This system is based on the decimal system. Each unit higher is 10 times the previous unit. For example, a kilometer is 10 times a hectometer, and a hectometer is 10 times a decameter, which is 10 times a meter.

When converting one unit into another, consider:

Is the unit, you are converting to, below or above the original unit? If it is above, divide by 10; if it is below, multiply by 10. Going down the list, each unit is 1/10 of the one above it. To convert a unit into the next smaller unit, multiply it by 10. Add a zero to 1 for each step. Look at the example below:

If we want to convert a kilometer to hectometer, we multiply it by 10 (1 followed by one zero since it is just the next unit). But if we want to convert a kilometer to a decameter, which is two steps below, we multiply by 100 (1 followed by two zeros). To convert a kilometer to millimeters, we multiply by 1,000,000 (1 followed by six zeros as millimeter is six steps below the kilometer).

If we want to convert a smaller unit into the next higher unit, we divide it by 10. As in the example above, for each step we add a zero to one and then divide. For example, if we want to convert a millimeter to a meter, we divide it by 1,000 (1 followed by three zeros as meter is three steps above the millimeter).

When converting smaller units to larger units, decimals come in very handy. As you already know, when we divide a number by ten, we shift the decimal one place to the left. For example, if you want to divide 35 by 10, you don't need to actually divide the number. You simply put a decimal between 3 and 5. In a whole number you do not see the decimal. But in fact it is just the same as 35.0. So we move the decimal to the left, and get 3.5.

If you want to covert 35 centimeters to meters, you need to divide it by 100. So you place the decimal two places to the left, to get your answer of 0.35 meters.

In multiplying a number by 10, 100, etc., we move the decimal to the right as many place, as there are zeros in the multiplicand. If there is no decimal in the number, then we add as many zeros as in the multiplicand to the product. For example, if you want to multiply 3.05 by 10, you would move the decimal one place to the right. This will give you 30.5 as your product. But if you have to multiply 305 by ten, and there is no decimal, you would add a zero to the number to get 3050 as the product.

Now look at a few more examples to understand the relationship between the units of distance.

Bill walks to a rice store which is 1.05 kilometers away. How many meters does he walk each way?

Here you have to convert kilometers (km) to meters (m). Meter is a unit which is three steps below kilometer. So we multiply by 1000 (1 followed by three zeros). This is how it is done:

1.05 km = 1.05 x 1000
= 1,050 m
(In order to multiply by 1000, we have moved the decimal three place to the right. Since we had only two digits - 0 and 5 - after the decimal, we have added another 0.)

An ant has to travel 1.75 m to its hole to carry a grain of rice from a pile. How many kilometers did it walk, if it carried 50 grains of rice to its hole?

In this question, we want to consider the return trip of the ant as well. The ant covered the distance 100 times to carry 50 grains of rice. Look at how it is done:

Total distance the ant covered in 50 trips = 1.75 x 50 x 2 m
= 1.75 x 100 m
= 175 m
= 175/1000 km
= 0.175 km

In this example, we have first multiplied 1.75 by one hundred, and moved the decimal two places to the right. Then, in order to convert meters to kilometers, we divided by 1,000, and moved the decimal three places to the left.

Now try the following:

Every day, Robert has to drive 150 kilometers each way to reach his Louisiana rice farm. How many hectometers does he cover in 20 days? Charles works at a Texas rice store, which is at a distance of 580 m from his home. How many decameters does he walk in ten days? (Consider his coming and going both ways.) David works at a rice processing mill in California. From the mill section to the warehouse it is a distance of 1.25 km. If he makes 10 trips in a day (consider coming and going), how many decimeters does he cover?

Fred works at a restaurant in Missouri, where he serves his guests a variety of rice dishes. He has to walk a different distance to take each dish to the service counter. The distance that he covers for each dish is as follows:

Rice pilaf - 5 m
Risotto - 3.9 m
Rice noodles - 2.0 m

If he serves 20 rice pilafs, 10 risottos, and 50 rice noodles, compute in kilometers the distance that he walks in a day.

George's California rice farm is 1,800 m long and 1,200 m wide. How many kilometers does he walk, if in a day he has to go around the farm five times while performing different rice cultivation jobs?




ACTIVITIES




Walk to a nearby grocery store and find the rice section. Count the steps you have to walk each way. Count each step as 30 centimeters, compute the
distance to the store and back in kilometers.












EXTENDED LEARNING

Identify ten situations each, in which you would use kilometer, meter, centimeter or millimeter to measure distance or length.




VOCABULARY

  • immediate
  • multiplicand
  • product
  • particular
  • processing
  • mill
  • compute


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