Approximation & Conversion Techniques: Definition, Rules, Sample Questions, Tips and FAQs

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Vipra Shrivastava

Vipra ShrivastavaSenior Manager - Content

Updated on Sep 23, 2024 12:43 IST

Approximation and Conversion are a critical topic in Mathematics. For solving many Mathematical problems, conversion of units is required. For example, the height may be given in centimetres and width may be given in millimeters, and you have to find out the area. For that, you will need to know unit conversion. This is a very simple example, in MBA entrance exams and other competitive exams, a tough and multilayered questions are asked which require approximation and conversion.

What are Approximation & Conversion Techniques?

The conversion of units is a very crucial topic in Mathematics. Sometimes, the values of different attributes of any object are available in distinct units. So, it is necessary to convert these units into a single unit and then apply a formula to find the area, volume, surface area, etc. For example, there is a cuboid-shaped object with length and breadth in centimetre and height in meter. We need to find out the surface area in inches. To solve this, we need to convert all the units into inches and then find the surface area.

Inch Definition

An inch can be defined as a unit for measurement of length. It is denoted by the symbol 'in'.

Centimetre Definition

A centimetre is another unit of measuring the length. A Centimeter unit gets used for the measurement of the length and height of most of the objects. It is denoted as 'cm'.

About inches to centimetres

Unit conversion is a very crucial topic in Mathematics, so is the inches to centimetre conversion. It is because of multiple applications in different chapters of Physics and Mathematics that students will study in upcoming classes. So the basic conversion should be clear. As part of this topic, students are taught about units inches and centimetres and their interconversion. 

Inches to Centimeters Calculation

Both centimetres and inches are used to measure the height or the length of an object. Both these units are interchangeable. To convert the units, it is necessary to know the conversion values. Below are the relations between these two units.

  • 1 inch = 2.54 centimeters
  • 1 centimeter = 0.393 inches

By using the above conversion values, inches can be converted into centimetres and vice-versa. So, to convert any value from inch to centimetre, multiply the inch value by 2.54. Similarly, the centimetre can also get converted into inches by multiplying the cm value by 0.393.

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Illustrated Examples of Unit Conversion

Here are some illustrated examples to know how to convert units as given below:

Example 1: Convert 21 inches to centimetres.

Solution: As we know that 1 inch = 2.54 cms

Therefore, 21 inches = 21 x 2.54 = 50.4 cms

Example 2: A person having a height of 5 feet is 60 inches long. What will be the length of a person in centimetres who has a height of 5 feet?

Solution: Here 5 feet = 60 inch and 1 inch = 2.54 cm

Therefore, 60 inch = 60 * 2.54 cm = 152.4 cm

Example 3: Convert 3 inches to cms

Solution: 3 inches = 3 x 2.54 cms

Therefore, 3 inches = 7.62 cms

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What Are Decimals and Fractions?

Decimals are numbers that have a decimal point. They denote any fraction with the denominator ten or its multiples. They are an easier way of writing those fractions so that certain operations like addition, etc. can be done more quickly.

Fractions denote a part of a whole and can be written with any denominator or numerator in the form x/y where y0. These are written in many forms: Improper, Proper, and Mixed forms.

The central concept here is that these two are inter-convertible. You can convert a decimal to a fraction or vice versa. 

Steps to Convert Decimals to Fractions:

  1. Make a note of how many numbers are thereafter the decimal point or to the right side of the point.

  2. If there are x number of digits, then multiply and divide the number by 10x, and the decimal point is removed.

  3. Simplify the fraction obtained to its simplest form, and thus the decimal is successfully converted to a fraction.

Example: Convert 20.2 to a fraction.

20.2 has one number after the decimal point. So, multiply and divide by 10.

20.2 x 10/10 = 202/10

It is simplified by using 2, to get: 101/5

Hence the fraction form of 20.2 is 101/5

Repeating Decimals to Fractions:

We know how to convert a finite decimal to a fraction, but what about the infinite decimals also known as repeating decimals? Examples: 0.6666… or 0.72727272…

For this, there is another method to obtain the fraction.

Example: Convert 0.33333… into a fraction.

Let x= 0.33333.., the 10x= 3.333..

10x - x = 3.3333…- 0.3333…

9x = 3

x = 3/9 

Therefore, x = 1/3

Illustrated Examples:

  1. Convert 2.35 to fraction.

2.35 has to be multiplied and divided by 100 = 235/100 = 47/20

  1. Divide 6.4 by 2 using the conversion to fraction method.

6.4/2 can be written as 64/10 2

= 64/10 x 1/2 = 32/10

  1. Convert 0.45454545… to a fraction.

Let x= 0.454545…, 100x = 45.4545…

100x - x = 45.4545.. - 0.4545..

99x = 45

x= 45/99 = 5/11

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FAQs Related to Approximation & Conversion Techniques

Q: What is the size of an inch?

A: Approximately 2.5 centimetres make an inch.

Q: How many inches make 1 cm?

A: Approximately 0.393 inches are equal to 1 cm.

Q: What steps do we follow to convert one unit to another?

A: First of all, find the relation between the two units and find out the conversion value. Then multiply or divide the conversion value with the given unit value to convert the value into the desired units.

Q: Is there any specific rule used to convert units?

A: The rule of thumb used for unit conversion is that when converting the large unit to a smaller one, multiply, and when converting a small unit to the large, divide it.

Q: There is a square-shaped sheet with a length of 81 cm and a breadth of 70 cm. How to find the area of this sheet in square inches?

A: Here, the length and breadth are in cms, and we need an area in square inches. So, multiply the length and the breadth to get the area in square cm. Then convert this area into inches.

Q: Are decimals and fractions interconvertible? How?

A: Yes. Decimals can be converted to fractions by dividing and multiplying by 10x, where x is the number of digits after the decimal point. Fractions can be converted to decimals by dividing and adding a decimal point in the dividend and substituting zeros until the remainder is zero.

Q: Give examples of a few frequently used decimals and their corresponding fractions.

A: 0.5 = 1/2 0.66666…= 1/3 0.25 = 1/4 0.4 = 2/5 1.5 = 3/2

Q: What is the fraction of 2.0?

A: 2.0 is actually the number 2. There are no significant digits after the decimal point. Hence x = 0, 10x = 100 = 1 So, 2.0/1 = 2/1

Q: Can decimals be converted to fractions with the denominator 0?

A: No. Decimals are fractions with denominators ten or multiples of 10.

Q: Are decimals and fractions rational numbers?

A: Yes, both are rational numbers.

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