**Introduction**

The process of associating numbers with physical quantities and phenomena is what we call a system of measurement. We need to measure a lot of things in our real life such as the weight of a bag, the capacity of a jar, length of a table. etc. The word “measurement” is derived from the Greek word “metron,” which means a limited proportion. There are two different systems of measurement in place that are commonly in use –

**Metric system** – It is the international decimal system of weights and measures, based on the metre for length and the kilogram for mass that was adopted in France in 1795 and is now used officially in almost all countries.

**Definition of Mass**

**Mass is the amount of matter an object contains.** Mass is commonly measured by something how much it weighs. The more matter something has, the more it will weigh. It is important to understand here that the size of something does not determine how much mass an object has. A golf ball and a ping-pong ball are the same sizes however a ping-pong ball is hollow while a golf ball is solid. Therefore, the golf ball has more mass inside of it compared to a ping-pong ball.

**Definition of Conversion of Measuring Mass**

Conversion of one unit to another unit of measurement for the same quantity using multiplication/division by conversion factors is known as unit conversion. Therefore, conversion of measuring mass means converting the units of mass from one form to another, say kg ro grams, grams to pounds etc.

**Standard Unit to Measure Mass**

Recall that the mass of an object is the amount of material it contains. The standard unit to measure mass is “ gram “ we use “ kilogram “ and “ milligram “ to measure heavier and lighter objects respectively. For instance, we use “ kilogram “ to measure the weight of a person and “ milligram “ to measure the weight of a pack of chocolates.

**Metric System for measuring mass**

1 ounce is almost as light as a slice of bread. 1 pound is equal to 16 ounces. Imagine two medium-sized oranges, that’s about a pound. For bigger things we use a ton. 1 ton is equal to 2,000 pounds. Ounces, pounds, and tons are called customary units. Grams and kilograms are called metric units.

The following table shows the relationship between different units used for measuring the weight of different objects –

**Conversion Table**

10 milligrams ( mg ) = | 1 centigram ( cg ) | |

10 centigrams = | 1 decigram ( dg ) | = 100 milligrams |

10 decigrams = | 1 gram ( g ) | = 1,000 milligrams |

10 grams = | 1 dekagram ( dag ) | |

10 dekagrams = | 1 hectogram ( hg ) | = 100 grams |

10 hectograms = | 1 kilogram ( kg ) | = 1,000 grams |

1,000 kilograms = | 1 metric ton ( t ) |

**Pounds to Kilograms Conversion**

1 pound (lb) is equal to 0.45359237 kilograms (kg). This means that 1 lb = 0.45359237 kg. Below is the conversion table from pounds to kilogram.

Pounds (lb) | Kilograms (kg) | Kilograms + Grams ( kg + g ) |

0 lb | 0 kg | 0 kg 0 g |

0.1 lb | 0.045 kg | 0 kg 45 g |

1 lb | 0.454 kg | 0 kg 454 g |

2 lb | 0.907 kg | 0 kg 907 g |

3 lb | 1.361 kg | 1 kg 361 g |

4 lb | 1.814 kg | 1 kg 814 g |

5 lb | 2.268 kg | 2 kg 268 g |

6 lb | 2.722 kg | 2 kg 722 g |

7 lb | 3.175 kg | 3 kg 175 g |

8 lb | 3.629 kg | 3 kg 629 g |

9 lb | 4.082 kg | 4 kg 82 g |

10 lb | 4.536 kg | 4 kg 536 g |

20 lb | 9.072 kg | 9 kg 72 g |

30 lb | 13.608 kg | 13 kg 608 g |

40 lb | 18.144 kg | 18 kg 144 g |

50 lb | 22.680 kg | 22 kg 680 g |

60 lb | 27.216 kg | 27 kg 216 g |

70 lb | 31.751 kg | 31 kg 751 g |

80 lb | 36.287 kg | 36 kg 287 g |

90 lb | 40.823 kg | 40 kg 823 g |

100 lb | 45.359 kg | 45 kg 359 g |

1000 lb | 453.592 kg | 453 kg 592 g |

**Kilograms to Pounds Conversion**

1 kilogram (kg) is equal to 2.20462262185 pounds (lbs). This means that 1 kg = 2.20462262185 lb. Below is the conversion table from kilogram to pounds.

Kilograms ( kg ) | Pounds ( lb ) | Pounds+Ounces( lb + oz ) |

0 kg | 0 lb | 0 lb 0 oz |

0.1 kg | 0.220 lb | 0 lb 3.527 oz |

1 kg | 2.205 lb | 2 lb 3.274 oz |

2 kg | 4.409 lb | 4 lb 6.548 oz |

3 kg | 6.614 lb | 6 lb 9.822 oz |

4 kg | 8.818 lb | 8 lb 13.100 oz |

5 kg | 11.023 lb | 11 lb 0.370 oz |

6 kg | 13.228 lb | 13 lb 3.644 oz |

7 kg | 15.432 lb | 15 lb 6.918 oz |

8 kg | 17.637 lb | 17 lb 10.190 oz |

9 kg | 19.842 lb | 19 lb 13.470 oz |

10 kg | 22.046 lb | 22 lb 0.740 oz |

20 kg | 44.092 lb | 44 lb 1.479 oz |

30 kg | 66.139 lb | 66 lb 2.219 oz |

40 kg | 88.185 lb | 88 lb 2.958 oz |

50 kg | 110.231 lb | 110 lb 3.698 oz |

60 kg | 132.277 lb | 132 lb 4.438 oz |

70 kg | 154.324 lb | 154 lb 5.177 oz |

80 kg | 176.370 lb | 176 lb 5.917oz |

90 kg | 198.416 lb | 198 lb 6.657 oz |

100 kg | 220.462 lb | 220 lb 7.396 oz |

1000 kg | 2204.623 lb | 2204 lb 9.962 oz |

**Conversion of Larger unit to Smaller Unit**

To convert a larger unit into a smaller unit we multiply the units by 10, 100, 1000 or other multiples of 10 depending upon the units being converted into.

**Converting kilogram into gram**

Let us understand it through an example.

**Example**

Suppose we wish to convert 4 kg into grams

**Solution**

We are required to convert 4 kg into grams. Now from the conversion table, we know that 1 kg = 1000 g. this means that in order to convert every kg into grams we need to multiply it by 1000. Therefore,

4 kg = 4 x 1000 g = 4000 g

**Converting grams into milligrams**

Let us understand it through an example.

**Example**

Suppose we wish to convert 4 g 280 mg into grams

**Solution**

We are required to convert 4 g 280 mg into grams. Now from the conversion table, we know that 1 g = 1000 mg. this means that in order to convert every g into milligrams we need to multiply it by 1000. Therefore,

4 g 280 mg = ( 4 x 1000 + 280 ) mg = ( 4000 + 280 ) mg = 4280 mg

**Converting larger decimal units into smaller units**

Let us first recall how multiplication is performed in decimal numbers. It is important to understand that when multiplying by 10, the value of each digit increases 10 times and therefore moves one place to the immediate left. Multiplying by 100 increases the digits’ values by 100 times moving them two places to the left and multiplying by 1000 increases their value 1000 times and moves them three places to the left. Let us consider an example. Suppose we wish to multiply 7 by 10. We know that 7 x 10 = 70. Similarly 7 x 100 = 700 and 7 x 1000 = 7000

To convert a larger decimal unit into a smaller unit we multiply the units by 10, 100, 1000 or other multiples of 10 depending upon the units being converted into.

Let us understand it through an example.

**Example**

Suppose we wish to convert 1.5 kg into grams

**Solution**

We are required to convert 1.5 kg into grams. Now from the conversion table, we know that 1 kg = 1000 g. this means that in order to convert every kg into grams we need to multiply it by 1000. Therefore,

1.5 kg = 1.5 x 1000 g = 1500 g

**Conversion of Smaller unit to Larger Unit**

To convert a smaller unit into a larger unit we divide the units by 10, 100, 1000 or other multiples of 10 depending upon the units being converted into.

**Converting grams into kilograms**

**Example**

Suppose we wish to convert 3 g into kilograms

**Solution**

We are required to convert 3 g into kilograms. Now from the conversion table, we know that 1 g = 1 / 1000 kg. this means that in order to convert every g into kilograms we need to divide it by 1000. Therefore,

3 g = 3 / 1000 g = 0.003 g

**Converting milligrams into grams**

**Example**

Suppose we wish to convert 5732 mg into grams

**Solution**

We are required to convert 5732 mg into grams. Now from the conversion table, we know that 1 mg = 1 / 1000 g. This means that in order to convert every mg into grams we need to divide it by 1000. Therefore,

5732 mg = 5732 / 1000 g = 5.732 g

**Converting smaller decimal units into larger units**

Let us first recall how division is performed in decimal numbers. Dividing whole numbers and decimal numbers by powers of 10 has the opposite effect to multiplying. The value of the digits decreases as opposed to increasing and the digits move to the right as opposed to the left on a place value chart. Let us, for example, take the number 745 and divide it by 10. We will have 745 ÷ 10 = 74.5. Similarly, 745 ÷ 100 = 7.45 and 745 ÷ 1000 = 0.745

To convert a smaller decimal unit into a larger unit we divide the units by 10, 100, 1000 or other multiples of 10 depending upon the units being converted into.

Let us understand it through an example.

**Example**

Suppose we wish to convert 3.8 g into kilograms

**Solution**

We are required to convert 3.8 g into kilograms. Now from the conversion table, we know that 1 g = 1 / 1000 kg. This means that in order to convert every g into kilograms we need to divide it by 1000. Therefore,

3.8 g = 3.8 / 1000 kg = 0.0038 kg

**Solved Examples**

**Example 1** Sam, Peter and Henry bought 8.5 kg, 7.25 kg and 9.4 kg of fruits respectively from a fruit vendor. How much fruit did they buy in all? If there were 30 kg of fruits in both, find the weight of fruits left with the fruit vendor.

**Solution**** **Let us first define what is given and what needs to be calculated. We have been given that Sam, Peter and Henry bought 8.5 kg, 7.25 kg and 9.4 kg of fruits respectively from a fruits vendor. We need to find out –

a) How much fruits did they buy in all?

b) If there were 30 kg of fruits in both, find the weight of fruits left.

Let us find the answers to the above problems one by one.

Weight of fruits bought by Sam = 8.5 kg

Weight of fruits bought by Peter = 7.25 kg

Weight of fruits bought by Henry = 9.4 kg

The total weight of fruits bought by them = 8.5 kg + 7.25 kg + 9.4 kg

Note here that the given decimals are not like terms. Hence, we will first need them to be converted into like terms. Therefore, we now have,

Weight of fruits bought by Sam = 8.5 kg = 8.50 kg

Weight of fruits bought by Peter = 7.25 kg = 7.25 kg

Weight of fruits bought by Henry = 9.4 kg = 9.40 kg

Now that the terms are like terms, we can go ahead with the calculations.

Total fruits bought by Sam, Peter and Henry = 8.50 kg + 7.25 kg + 9.40 kg = 25.15 kg

**Hence, the total fruits bought by Sam, Peter and Henry =25.15 kg**

Now, let us solve the second part of the question. We have been given that there was 30 kg of fruits in the booth. How much fruits are left after Sam, Peter and Henry bought the fruits?

Therefore,

Total fruits with the fruits vendor = 30 kg

Fruits bought by Sam, Peter and Henry = 25.15 kg

Again, we can see here that the given decimals are not like terms. Hence, we will first need them to be converted into like terms. Therefore, we now have,

Total fruits in booth = 30 kg = 30.00 kg

Fruits bought by Sam, Peter and Henry = 25.15 kg

Now that the terms are like terms, we can go ahead with the calculations.

Fruits left in the booth = 30.00 kg – 25.15 kg

= 4.85 kg

**Hence, after Sam, Peter and Henry, 4.85 kg of fruits was left in the booth.**

**Example 2** A rickshaw-puller is carrying two persons weighing 52 kg 250 g and 37 kg 700 g. What is the total weight of the two persons carried by the rickshaw-puller?

**Solution** We have been given that a rickshaw-puller is carrying two persons weighting 52 kg 250 g and 37 kg 700 g. we need to find the total weight of the two persons carried by the rickshaw-puller. In order to find the total weight carried by the rickshaw puller, we need to add both the weights. So we have,

52 kg 250 g + 37 kg 700 g = 89 kg 950 g

Hence, the total weight pulled by the rickshaw puller is 89 kg 950 g

**Example 3** Mother had 350 grams of sugar. She used 200 grams for a cake. How much sugar did she have left in milligrams?

**Solution** We have been given that Mother had 350 grams of sugar. She used 200 grams for a cake. We need to find how much sugar she had left in milligrams. Let us first find the amount of sugar left in grams. We have,

Amount of sugar mother had = 350 g . . . . . . . . . . . . . . ( 1 )

Amount of sugar used for the cake = 200 g . . . . . . . . . . ( 2 )

Amount of sugar left in grams = ( 1 ) – ( 2 ) = 350 g- 200 g = 150 g

Now let us convert 150 g to mg

We know that 1 g = 1000 mg

Hence, 150 g = 150000 mg

**Therefore, amount of sugar left in milligrams = 150000 mg**

**Key Facts and Summary**

- The process of associating numbers with physical quantities and phenomena is what we call a system of measurement.
- The Metric system is the international decimal system of weights and measures, based on the metre for length and the kilogram for mass that was adopted in France in 1795 and is now used officially in almost all countries.
- Mass is the amount of matter an object contains. The more matter something has, the more it will weigh.
- 1 ounce is almost as light as a slice of bread. 1 pound is equal to 16 ounces. Imagine two medium-sized oranges, that’s about a pound. For bigger things we use a ton. 1 ton is equal to 2, 000 pounds. Ounces, pounds, and tons are called customary units. Grams and kilograms are called metric units.
- Weight is the measure of the quantity of an object.
- The mass of an object is the amount of material it contains.
- To convert a larger unit into a smaller unit we multiply the units by 10,100,1000 or other multiples of 10 depending upon the units being converted into.
- To convert a smaller unit into a larger unit we divide the units by 10,100,1000 or other multiples of 10 depending upon the units being converted into.

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