A coconut tree grows up to 15 m, whereas, a plum tree grows up to 25 feet. Comparing the heights of both the trees is not easy as their units of measurements are different. To ease this comparison, convert one of the units as the other. **The process of changing the values from one form to the other to ease the calculations is called conversion.** In mathematics, the conversions usually occur between the parameters such as lengths, weights, angles, temperatures, areas, volumes, and time.

## Conversion of Units

It is the process of multiplying or dividing one unit by another to convert different units and measures of the same quantity. The quantities that we use to convert are listed below.

There are non-standard units of measurements, that is, hand and foot. Consider an example of measuring the length of a pencil.Stretch the fingers of your hand wide; the distance from the tip of your thumb to the top of the little finger is 1 hand span. Place the pencil against your foot; the distance between the tip of the big toe to the end of the heel of human foot is 1 foot. Refer to the image below.

## Conversion Factors

A conversion factor is a quantity or a number which is used to convert one set of units to another by multiplying or dividing them. Calculation is made simple and quick with the use of an appropriate conversion factor.

### Conversions of measurements

The process of converting measurements of objects from one unit to another is known as measurement conversion. For instance, meters can be converted to centimeters, miles to meters, feet to inches, and so on. For comparing measurements on different scales, length conversion is required.

**A metric system is a unit of measurement adopted by most of scientists and mathematicians all over the world.** All metric measurement units contain the words meter, liter, or gram as the base word. To understand conversion of length, let us consider the basic unit for metric conversion is as 1 meter.

To convert a larger unit to a smaller unit, the units are multiplied by a conversion factor; to convert a smaller unit to a larger unit, the units are divided by a conversion factor. Multiplication and division by 10 are the foundations of the system. Let us see the steps to convert the unit which is called as a Ladder method. Refer to the images given below.

### How do you use the ladder method?

The correct use of the ladder method can be done using the steps shown below.

1. Determine the starting point (the unit which you want to convert).

2. Count the jumps to your ending point (the number of steps it takes).

3. Move the decimal the same number of jumps in the same direction.

### Examples of conversion of length units

**Example 1: Convert 6 meter to centimeter.**

**Solution:** 1 meter = 100 centimeter

⇒ 6 meter = 6 × 100 = 600 centimeter

**Example 2: Convert the following.
a) 3 km to m
b) 5000 m to km**

**Solution:** 1 km = 1000 m or 1000 m = 1 km

a) 3 km = 3 × 1000 = 3000 m

b) 5000 m = 5000 / 1000 = 5 km

**Example 3: Convert the following.
a) 40 mm to cm
b) 2500 mm to m**

**Solution:** 1 cm = 10 mm, 1 mm = 1/10 cm, and 1 mm = 1/1000 m

a) 40 mm = 1/40 cm = 0.4 cm

b) 2500 mm = 2500/1000 = 2.5 m

**Always Remember!**

**Anything longer than 1 meter is a multiple of the meter.**

**kilo –** is a prefix for thousand, so a kilometer is 1000 meters.

For example, 6 kilometers = 6000 meters

**Anything shorter than 1 meter is a part of a meter.
centi** – is a prefix for one-hundredth, so a centimeter is 1/100 of a meter.

**milli**– is a prefix for one-thousandth, so millimeter is 1/1000 of a meter.

## Examples of Conversion of Mass units

The weight of an object is measured by mass. In a metric system, the most common units of mass are kilogram, gram, quintal, and ton. Refer to the image below.

**Example 4: Convert 12 kg to g.**

**Solution:** 1 kg = 1000 g

12 kg = 12 × 1000 = 12,000 g

**Example 5: Convert the following.
a) 8500 mg to g
b) 1500 g to mg
c) 80,000 g to kg**

**Solution:**

a) 1 mg = 1/1000 g

8500 mg = 8500/1000 = 8.5 g

b) 1 g = 1000 mg

1500 g = 1500 × 1000 = 1,500,000 mg

c) 1 g = 1/1000 kg

80,000 g = 80,000/1000 = 80 kg

**Example 6: Tina goes to market to buy vegetables. She bought 2500 g of tomatoes, 3200 g of onions, 1500 g of carrot, and 200 g of chilies. What is the total weight of vegetables Tina bought, in kg, from the market?**

**Solution:** To find the total weight of vegetables add all the weights of vegetables.

## Conversion of Capacity units

The amount each bottle can hold is called its capacity. We have different units to measure the capacity. Capacity can be measured in millilitre (ml) and litre (l). Refer to the image below.

**Example 7: Convert the following.
a) 21 kl to l
b) 51,000 ml to l**

**Solution: **1 kl = 1000 l, 1 l = 1/1000 ml

a) 21 kl = 21 × 1000 = 21,000 l

b) 51,000 ml = 51,000/1000 = 51l

**Example 8: Sarah prepared 4 liters and 500 ml of juice in a jug. She shared equally into 18 glasses. How much juice is there in each glass?**

**Solution:** 4 liters and 500 ml = 4500 ml

Juice is poured equally in 18 glasses.

Each glass contains 4500/18 = 250 ml of juice.

### Conversion of Time

In science and technology, time conversion is essential. Every second spent browsing or collecting data has a significant economic impact. We must convert time into one of the forms to compare the same event occurring at various times. To convert bigger unit to smaller unit, we should multiply. To convert smaller unit to bigger unit, we should divide.

**Example 9: Convert 540 seconds into minutes.**

**Solution:** To convert smaller unit to bigger, we should divide.

60 seconds = 1 minute

540 seconds = 540/60 = 9 minutes

**Example 10: Convert 4.5 hours to seconds.**

**Solution:** To convert bigger unit to smaller, we should multiply.

1 hours = 60 × 60 = 3600 seconds

4.5 hours = 4 hours 30 minutes

4 hours = 4 × 3600 = 14,400 seconds

1 minute = 60 seconds

30 minutes = 30 × 60 = 1800 seconds

Therefore, 4.5 hours = 14,400 + 1800 = 16,200 seconds.

Conversion of time involves not only hours, minutes, and seconds. We can also convert years to days, months, weeks, hours and so on. Refer to the image below.

**Example 11: Convert the following.
a) 52 months to years and months
b) 489 days to weeks and days
c) 11 days to minutes**

**Solution:**

a) 12 months = 1 year

52 months = 48 months + 4 months

= 48/12 = 4 years + 4 months

Therefore, 52 months is 4 years 4 months.

b) 7 days = 1 week

489 days = 463 days + 6 days

= 483/7 + 6 days

= 69 weeks 6 days

Therefore, 489 days is 69 weeks 6 days.

c) 1 day = 24 × 60 = 1,440 minutes

11 days = 11 × 1440 = 15,840 minutes

Therefore, 11 days is 15,840 minutes.

## Math Facts about Unit Conversions

## James Clerk Maxwell – Mathemagician of Unit Conversions

The metric system began with natural length and weight measurements, as well as their decimal multiples and fractions, during the Age of Enlightenment. The metric system was initially put into practice in 1799, during the French Revolution, when the old system of measurements became impracticable for trade and was replaced by a decimal system based on the kilogram and the meter. Natural elements were used to create the fundamental units. The meter, a measure of length, was based on the dimensions of the Earth, whereas the kilogram, a unit of mass, was based on the mass of one liter of water (a cubic decimeter).

James Clerk Maxwell proposed a coherent system in the mid-nineteenth century, in which a small number of units of measure were specified as base units, and all other units of measure, known as derived units, were defined in terms of the base units. For length, mass, and time, Maxwell proposed three base units. Advances in electromagnetism in the nineteenth century prompted the definition of additional units, and numerous incompatible systems of such units were developed; none of them could be reconciled with the current dimensional system.

Know more about other concepts of Number Systems on Fibonacci Numbers, Types of Fractions, Natural Numbers, Prime Numbers and Whole Numbers.

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