For the conversion of standard unit of mass it’s very important to know the relationship between the different units of mass.
Standard unit of weight is gram (g). Kilogram is a bigger unit to measure weight.
1 kilogram = 1000 gram or 1 kg = 1000 g
1000 grams = 1 kg
Two 500 grams = 1 kg
Five 200 grams = 1 kg
Ten 100 grams = 1 kg
Thus, 1 kg = Two 500 g = Five 200 g = Ten 100 g
There are some higher units named quintal and metric ton for measuring the mass of heavier things.
1 quintal = 100 kilogram
1 metric ton = 1000 kilogram
Thus, 1 metric ton = 10 quintal
Hence, one metric ton = 10 quintal or ten 100 kg = 1000 kg
To weigh lighter objects we use grams (g) and to measure heavier objects we use kilograms (kg).
Conversion of one unit of mass into another:
Let us learn how to convert kilograms into grams and grams into kilograms.
How to convert one unit of mass into another?
To convert kilograms into grams, we write three zeroes (000) towards the right of the number of kg. (since, 1 kg = 1000 g)
I. Conversion of kilograms into grams:
To convert kilograms into grams, we will multiply the number of kilograms by 1000.
1 kg = 1000 g
For example:
1. Convert 6 kg into grams.
Solution:
1 kg = 1000 g
6 kg = 6 × 1000 = 6000 g
2. Convert 8 kg into grams.
Solution:
1 kg = 1000 g
8 kg = 8 × 1000 = 8000 g
Note: To convert kilograms (kg) into grams (g) simply we need to add three zeros to the right.
II. Conversion of grams into kilograms:
To convert grams into kilograms, we will divide the number of grams by 1000.
1 g = \(\frac{1}{1000}\) kg
For example:
1. Convert 2000 grams into kilograms.
Solution:
1 g = \(\frac{1}{1000}\) kg
2000 g = \(\frac{2000}{1000}\) kg = 2 kg
2. Convert 4000 grams into kilograms.
Solution:
1 g = \(\frac{1}{1000}\) kg
4000 g = \(\frac{4000}{1000}\) kg = 4 kg
3. Convert 6000 grams into kilograms.
Solution:
1 g = \(\frac{1}{1000}\) kg
6000 g = \(\frac{6000}{1000}\) kg = 6 kg
Note: To convert grams (g) into kilograms (kg), simply we need to remove three zeros from the end of the number.
Conversion of kilograms and grams into grams:
To convert kilograms and grams into grams, we will multiply the number of kilograms by 1000 and add it to the number of grams.
For example:
1. Convert 3 kg 350 g into grams.
Solution:
1 kg = 1000 g
3 kg = 3 × 1000 = 3000 g
3 kg 350 g = 3000 + 350 = 3350 grams
2. Convert 9 kg 325 g into grams.
Solution:
1 kg = 1000 g
9 kg = 9 × 1000 = 9000 g
9 kg 325 g = 9000 + 325 = 9325 grams
3. Convert 2 kg 250 g into grams.
Solution:
1 kg = 1000 g
2 kg = 2 × 1000 = 2000 g
2 kg 250 g = 2000 + 250 = 2250 grams
Conversion of grams into kilograms and grams:
To convert grams into kilograms and grams, we will divide the number of grams by 1000. The quotient represents kilograms and the remainder represents gram.
For example:
1. Convert 7150 grams into kilograms and grams.
Solution:
7150 g = 7000 + 150 g
7150 g = 7 kg 150 g
A shortcut method to convert grams into kilograms is to write three digits from right as grams and the remaining as kilograms.
For example, we write 7150 g as 7 kg 150 g.
Worked-out problems on conversion of standard unit of mass into another:
1. Convert the following into grams:
(i) 28 kg
We know, 1 kg = 1000 g
= (28 × 1000) g
= 28000 g
Therefore, 28 kg = 28000 g
(ii) 12 kg 58 g
We know, 1 kg = 1000 g
= (12 × 1000) g + 58 g
= 12000 g + 58 g
= 12058 g
Therefore, 12 kg 58 g = 12058 g
(iii) 15 kg 465 g
We know, 1 kg = 1000 g
= (15 × 1000) g + 465 g
= 15000 g + 465 g
= 15465 g
Therefore, 15 kg 465 g = 15465 g
2. Express the following in kilogram and grams:
(i) 3567 kg
We know 1000 g = 1 kg
First three digits 5, 6 and 7 are taken as grams
= 3 kg 567 g
Therefore, 3567 g = 3 kg 567 g
(ii) 45600 g
We know 1000 g = 1 kg
First three digits 6, 0 and 0 are taken as grams and rest 45 as kg
= 45 kg 600 g
Therefore, 45600 g = 45 kg 600 g
(iii) 23817 g
We know 1000 g = 1 kg
First three digits 8, 1 and 7 are taken as grams and rest 23 as kg
= 23 kg 817 g
Therefore, 23817 g = 23 kg 817 g
These examples will help us to understand how to solve the conversion of standard unit of mass into another unit from kilogram into gram and also to express from grams to kg and g.
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