6th Grade - Math

LESSON PROBLEM: Measurement: If you are asked to quickly convert a weight given in decagrams into decigrams, or a weight given in milligrams into centigrams, how would you


STUDY GUIDE

The gram is the basic unit of weight. But we do not always use grams to measure weight. It depends on the thing that we have to weigh. In the decimal system, or metric system, we have units that increase or decrease in multiples of 10. The gram is the basic unit. We have weight measuring units that are 10, 100 or 1,000 times that of a gram. On the other hand we have units which are 1/10, 1/100, or 1/1,000 of a gram.
These are arranged in decreasing order below:

1 kilogram is 1000 grams.
1 hectogram is 100 grams.
1 decagram is 10 grams.
The gram is the basic unit of mass.
1 decigram is 1/10 gram.
1 centigram is 1/100 gram.
1 milligram is 1/1,000 gram.

As we move up the units, each unit is 10 times the weight of the one below it. And as we move down the units, each unit is 1/10 the weight of the one above it.

So, one kilogram is 10 times the weight of a hectogram. And a hectogram is 10 times the weight of a decagram. We can also say it in a different way: One hectogram is 1/10 of a kilogram. And a decagram is 1/10 of a hectogram.

When you need to convert one unit into another, you have to ask:

1.Are you going up or down? If you convert a unit into the one above it, divide by 10. For example, if you convert 20 decigrams into grams, divide it by 10. The answer is 2. So 20 decigrams are equal to 2 grams.
2.If you convert a unit into one below it, multiply by 10. For example, if you convert 3 kilograms to hectograms, multiply 3 by 10. This would give you 30 as your answer. So 3 kilograms are equal to 30 hectograms.

If you are going up or down by more than one step, then you have to divide or multiply by an additional 10 for each step. For example, if you are missing one unit in between, and you want to convert a unit to a second higher or lower unit, then divide or multiply it by 100 (10 x 10). In fact, you can just add an additional zero to 1 for each step. Look at the table of units below:

1.Kilogram
2.Hectogram
3.Decagram
4.Gram
5.Decigram
6.Centigram
7.Milligram

Here there are 7 steps in all. If you want to convert a kilogram to a milligram, there 6 steps in between. So, multiply the kilogram unit by 1 and 6 zeros. This means 1 kilogram = 1 x 1,000,000 = 1,000,000 milligrams.

Similarly, if you want to convert milligrams into kilograms, divide by 1,000,000.

You may sometimes be unsure of whether you are to multiply or to divide. For this there is a simple test. Just think whether you are converting into smaller units or bigger units. To convert to smaller units, you multiply, and to convert to a bigger unit, you divide. Look at the examples below:

You have 5 kilograms of long grain rice, which you want to portion out to contestants at a rice cooking competition. Each portion is 1 hectogram. How many contestants can get a portion of rice?

To solve this problem, convert the 5 kilograms to hectograms. Since the hectogram is the next lower unit, multiply by 10. 50 is our answer. So there is enough rice for 50 contestants.

At a rice cultivation show, the Rice Institute wanted to distribute 10-gram pouches of different varieties of rice among the students. They wanted to distribute 5,000 pouches. How much rice was required for this purpose?

To solve this problem, first think of 10-gram pouches as 1-decagram pouches. You might want to multiply 5,000 pouches by 10, to find the quantity in grams. But if we think of 10 grams as a decagram, then we can skip that step.

So we need 5,000 decagrams of rice. Now look at the table above. To find the answer in kilograms, divide it by 100 (we are skipping one unit in between). So we need 50 kilograms of rice for the pouches.

Now convert the following units(use decimals for fractions):

1.2 kilograms to hectograms
2.9 decagrams to decigrams
3.6 grams to milligrams
4.7 decigrams to centigrams
5.12 milligrams to grams
6.45 decagrams to centigrams
7.789,987 milligrams to kilograms
8.9 kilograms to centigrams
9.3 kilograms to milligrams
10.897 centigrams to decagrams




ACTIVITIES

Visit a store and look for the mass of different rice product packages. Convert their masses into smaller or bigger units just by multiplying or dividing by 10, 100 or 1,000 as required. Use decimals wherever you can.




EXTENDED LEARNING

Convert one unit into another using by moving only the decimal point. Do not actually multiply or divide by 10, 100 or 1,000.




VOCABULARY

  • mass
  • convert
  • decimal system
  • decreasing
  • pouch
  • skip
  • gram



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