Word Problems on Conversion of Units: Conversion of units is a multi-step process that involves multiplication or division by a numerical factor. In Mathematics, while solving numerical problems, it is required to convert the units. Thus the conversion of units should be needed to solve the required calculations wherever it is necessary.

For example, if we need to calculate the area of the rectangle, in which length is given in centimetres \(\left( {{\rm{cm}}} \right)\), and the width is given in metres \({\rm{m}}\), then it is necessary to convert any one unit either length or width, so that both the units become the same.

Therefore, to solve the word problems in mathematics, learning the conversion of units is necessary. This article will discuss the conversion of units in more detail.

Definition of Word Problems on Conversion of Units

Conversion of units is a multi-step process that involves multiplication or division by a numerical factor. Word problems on the conversion of units consist of a few sentences describing a real-life scenario where mathematical definitions and concepts of converting units from one unit to another unit are used to solve a problem.

The conversion of units may also require selecting the correct number of significant digits and rounding off. In mathematics, we convert the units from one unit to the other unit for better understanding. 

For example, the length of a garden is measured in yards, whereas the length of a table is measured in inches. But we cannot measure the length of a finger in miles. To measure different quantities, different units of measurements are needed.

The conversion of units should be needed to solve the required calculations wherever it is necessary. For example, if we need to calculate the area of the rectangle, in which length is given in centimetres \(\left( {{\rm{cm}}} \right)\), and the width is given in metres \(\left( {{\rm{m}}} \right)\), then it is necessary to convert any one unit, either length or width, to make them uniform.

Converting Metric Units Word Problems

In mathematics, we have metric systems such as measuring units of length and distance, weight, and capacity. As we discussed, to solve the word problems correctly, we need to learn the conversion of units, and it is necessary too.

The metric system was introduced in France in the year \(1790\). The metric system of measuring units is based on the decimal system. The base units for length is metre, for weight kilogram and seconds for the time.

Unit conversion is a multi-step process that involves multiplication or division by a numerical factor. To convert any bigger unit to a smaller unit, we should multiply with the conversion factor. Similarly, to convert any smaller unit to a bigger unit, we should divide it with the conversion factor.

Word Problems on Conversion of Units of Length

Length is a one-dimensional scalar quantity, which measures the line segment. The basic unit used for measuring the length is a metre \({\rm{(m)}}\). Depending on the specimen or object used for measurement, we have different types of units like \({\rm{cm,}}\,{\rm{km,}}\,{\rm{inches,}}\,{\rm{ft}}\), etc.

For example, the length of a garden is measured in yards, whereas the length of a table is measured in inches. But we cannot measure the length of a finger in miles. To measure different quantities, different units of measurements are needed. 

The below chart gives the conversion of length:

To convert a unit from a metre to a centimetre, we should multiply by \(100\) such that \(1\,{\rm{m}}\, = \,100\,{\rm{cm}}\)

Example:

Asit and Keerthi each ran on a treadmill exactly for \(90\) minutes. Asit’s treadmill showed he had run \(18500\) meters. Keerthi’s treadmill showed she had run \(20\) kilometres. Who ran farther, and how much?

The time took by the Keerthi and Asit are the same, that is \(90\) minutes.

Here, the distance covered by Asit and Keerthi has different measuring units. For uniformity in the calculation, we have to convert the units from \({\rm{km}}\) to \({\rm{m}}\) or \({\rm{m}}\) to \({\rm{km}}\).

Let us convert \({\rm{km}}\,\) to \({\rm{m}}\,\).

So, the distance covered by the Asit on the treadmill \( = 18,500\,{\rm{m}}\)

And, the distance covered by the Keerthi on treadmill \( = 20\,\,{\rm{km}}{\rm{ = }}{\rm{20}} \times {\rm{1000}}{\rm{m  = }}{\rm{20,}}\,{\rm{000}}\,{\rm{m}}\)

The difference in their distances is \({\rm{20,}}\,{\rm{000}}\,{\rm{m}}\,{\rm{ – }}\,{\rm{18500}}\,{\rm{m}}\,{\rm{ = 1500}}\,{\rm{m}}\)

So, Keerthi ran farther as compared with Asit by \({\rm{20,}}\,{\rm{000}}\,{\rm{m}}\,{\rm{ – }}\,{\rm{18500}}\,{\rm{m}}\,{\rm{ = 1500}}\,{\rm{m}}\)

So, Keerthi ran farther as compared with Asit by \({\rm{1500}}\,{\rm{m}}\) or \({\rm{1.5}}\,{\rm{km}}\).

Word Problems on Conversion of Units of Weight

Weight is the one-dimensional vector quantity, which is used for the measurement of objects. Generally, the weight of the object is measured in the base unit kilogram \(\left( {{\rm{kg}}} \right).\)  We know that weight of the person is measured in \({\rm{(kg)}}\) and the weight of the small pieces of gold is measured in grams. So, it is important to convert the units of the weights while solving word problems for uniformity in the calculation.

The below figure shows the conversion of weights from one unit to another unit:

Example:

Nag is carrying \(2.5\,{\rm{kg}}\) of apples and \(5\,{\rm{g}}\) of carrying bag. Find the total weight she is holding in her hand.

The total weight \( = 2.5 \times 1000\,{\rm{g}}\,{\rm{ +  5g}}\,{\rm{ = }}\,{\rm{2505}}\,{\rm{g}}\)

Word Problems on Conversion of Units of Time

We know that seconds are the basic unit for measuring time. We have to convert the units of time from one unit to another unit for solving the problems. The below chart gives the conversion of time:

Example:
The time taken to reach the shop is \(30\) minutes and from the due to heavy traffic, the time taken to reach the house is \(1\) hour. Find the total time taken?

The total time taken \( = 30\min {\rm{utes}} + 1 \times 60\min {\rm{utes}} = 90\min {\rm{utes}}\,\)

Word Problems on Conversion of Units of Area

The area is the two-dimensional property. We have different units for measuring the area. The below figure shows the conversion of area units:

Example:

The area of the parking lot is \(12{{\rm{m}}^2}\) and \(50\,{\rm{c}}{{\rm{m}}^{\rm{2}}}\) Find the total area?

The total area \( = \,12\, \times \,{100^2}\,{\rm{c}}{{\rm{m}}^2}\, + \,500\,{\rm{c}}{{\rm{m}}^2}\, = \,1440000\, + 500\, = \,1440500\,{\rm{c}}{{\rm{m}}^2}\)

Word Problems on Conversion of Units of Capacity

Capacity describes the volume of the object. The different types of units used for measuring the capacity are given below:

Example:

The capacity of the water bottle is \(1\,{\rm{l}}\) and the cap is \(1\,{\rm{ml}}\) Find the total capacity of the bottle.

The total capacity \( = 1 \times 1000\,{\rm{ml}} + 1\,{\rm{ml}} = 1001\,{\rm{ml}}\)

Solved Examples – Word Problems on Conversion of Units

Q.1. The distance between the two places in a city is \(31,\,680\, feet\) Express the distance in miles.
Ans: Given the distance between the places \({\rm{ = 31,680}}\,{\rm{feet}}\)
We know that \({\rm{1feet}} = \frac{1}{{5280}}{\rm{miles}}\)
So, total distance in miles \( = \frac{{31,680}}{{5280}} = 6\,{\rm{miles}}\)

Q.2. Asit’s mom took \(30\) minutes to cut the vegetables, and she took \(1\) hour in cooking. Find how many minutes she took to complete the whole cooking?
Ans: The time taken for cutting the vegetables \( = 30\,{\rm{minutes}}\)
The time taken for cooking \( = 1\,{\rm{hour}} = 60\,{\rm{minutes}}\)
Total time taken for whole cooking \( = \,30\, + \,60\, = \,90\,{\rm{minutes}}\)

Q.3. Vicky has \(14,500\,{\rm{g}}\) of sand in his sandbox, and he bought \(7500\,{\rm{g}}\) of sand from the beach. Total how many kilograms of sand Vicky has in his sandbox.
Ans:Initial sand in the box is \(14,500\,{\rm{g}}\,{\rm{ = }}\,\frac{{14,500}}{{1000}}\,{\rm{kg}}\, = \,14.\,5\,{\rm{kg}}\)
The sand bough from the beach \( = 7500\,{\rm{g}}\,{\rm{ = }}\,\frac{{7500}}{{1000}}\,{\rm{kg}}\, = \,7.\,5\,{\rm{kg}}\)
Total sand in the box \( = 14.5\,{\rm{kg}}\,{\rm{ + }}\,7.5\,{\rm{kg}}\, = \,22\,{\rm{kg}}\)

Q.4. Jessica measures two line segments. The first line segment is \(30\,{\rm{cm}}\) long. The second line segment is \(500\,{\rm{mm}}\) long. How long are the two line segments together? (answer in cm)
Ans: The length of the first line segment \( = \,\,30\,{\rm{cm}}\)
The length of the second line segment \({\rm{ = }}\,{\rm{500}}\,{\rm{mm}}\,{\rm{ = }}\,\frac{{500}}{{10}}\,{\rm{cm}}\,{\rm{ = }}\,{\rm{50}}\,{\rm{cm}}\)
The total length of two-line segments \( = \,\,30\,{\rm{m}}\,{\rm{ + }}\,{\rm{50}}\,{\rm{m}}\, = \,80\,{\rm{m}}\)

Q.5. The length of the box is \(2\,{\rm{m}}\) and the width is \(40\,{\rm{cm}}\) Find the area of the box in \({\rm{c}}{{\rm{m}}^2}\)
Ans: Given the length of the box \(2\,{\rm{m}}\)
Width of the box \({\rm{ = }}\,{\rm{40}}\,{\rm{cm}}\)
Area of the box \({\rm{ = }}\,{\rm{length}}\, \times \,{\rm{width}}\,{\rm{ = }}\,{\rm{200}}\,\, \times \,40\, = \,8000\,{\rm{c}}{{\rm{m}}^2}\)

Summary

In this article, we have discussed various methods of the conversion of units from one unit to another unit. This article also discusses the conversion of metric units and word problems on the conversion of metric units.
In this article, we have studied the word problems on the conversion of units of length, weight, area, time and capacity, along with the solved examples that help us solve the numerical problems easily.

Frequently Asked Questions – Word Problems on Conversion of Units

Q.1. How do you solve unit conversion problems?
Ans: The following steps are to be followed to do unit conversion problems.
1. Read the data and the given units.
2. Now, multiply or divide as required conversion with the conversion factor.
3. Then, solve the problems using the proper formulas and operations.

Q.2. How do you solve metric word problems?
Ans: The metric word problems are to be solved by using the unit conversion. Convert any bigger unit to the smaller unit, and we should multiply with the conversion factor. Similarly, to convert any smaller unit to a bigger unit, we should divide it with the conversion factor.

Q.3. Why is unit conversion important?
Ans: To solve many real-life problems, unit conversion is very important because we cannot perform basic operations like addition, subtraction, multiplication, division etc., unless the two quantities are in the same units.

Q.4. What are the three basic metric units?
Ans: The three basic metric units are metre for length, gram for weight and litre for capacity.

Q.5. What is unit conversion?
Ans: Conversion of units is a multi-step process that involves multiplication or division by a numerical factor.

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