Grade 10
  1. Number Systems  1.1. Real Numbers  1.1.1. Properties of Real Numbers  1.1.2. Rational and Irrational Numbers  1.1.3. Decimal Representation of Real Numbers  1.1.4. Operations on Real Numbers  1.1.5. Real Numbers on the Number Line  1.2. Euclid's Division Lemma  1.3. Prime Factorization  1.4. LCM and HCF  1.5. Exponents and Radicals  1.5.1. Laws of Exponents  1.5.2. Simplifying Radical Expressions  1.5.3. Scientific Notation
  2. Algebra  2.1. Polynomials  2.1.1. Definition and Types of Polynomials  2.1.2. Degree of a Polynomial  2.1.3. Zeros of a Polynomial  2.1.4. Factorization of Polynomials  2.1.5. Algebraic Identities  2.2. Linear Equations in Two Variables  2.2.1. Graph of Linear Equations  2.2.2. Solutions of Linear Equations  2.2.3. Application of Linear Equations in Word Problems  2.3. Quadratic Equations  2.3.1. Standard Form of a Quadratic Equation  2.3.2. Methods of Solving Quadratic Equations  2.3.2.1. Factorization Method  2.3.2.2. Completing the Square Method  2.3.2.3. Quadratic Formula  2.3.3. Nature of Roots  2.4. Arithmetic Progressions  2.4.1. Definition of Arithmetic Progression  2.4.2. General Term of an AP  2.4.3. Sum of First n Terms of an AP  2.5. Introduction to Functions  2.5.1. Definition and Types of Functions  2.5.2. Domain and Range  2.5.3. Composition of Functions  2.5.4. Inverse of a Function
  3. Coordinate Geometry  3.1. Cartesian System  3.2. Distance Formula  3.3. Section Formula  3.4. Area of a Triangle  3.5. Slope of a Line  3.6. Equation of a Line  3.6.1. Slope-Intercept Form  3.6.2. Point-Slope Form  3.6.3. Two-Point Form  3.6.4. Intercept Form  3.6.5. General Form of a Line
  4. Trigonometry  4.1. Trigonometric Ratios  4.1.1. Sine Cosine Tangent and their Reciprocals  4.1.2. Values of Trigonometric Ratios at Specific Angles  4.2. Trigonometric Identities  4.3. Trigonometric Ratios of Complementary Angles  4.4. Heights and Distances  4.4.1. Angle of Elevation and Depression  4.4.2. Applications in Real-Life Problems
  5. Geometry  5.1. Triangles  5.1.1. Congruence of Triangles  5.1.2. Criteria for Congruence  5.1.3. Properties of Triangles  5.2. Similarity  5.2.1. Similar Figures  5.2.2. Criteria for Similarity  5.2.3. Similarity of Triangles  5.2.4. Applications of Similarity in Real-Life  5.3. Circles  5.3.1. Properties of a Circle  5.3.2. Tangent to a Circle  5.3.3. Number of Tangents from a Point  5.3.4. Angle Subtended by an Arc  5.4. Constructions  5.4.1. Construction of Similar Triangles  5.4.2. Tangent to a Circle  5.4.3. Construction of Angle Bisectors
  6. Mensuration  6.1. Areas of Plane Figures  6.1.1. Area of a Triangle  6.1.2. Area of a Parallelogram  6.1.3. Area of a Trapezium  6.1.4. Area of a Rhombus  6.2. Surface Areas and Volumes  6.2.1. Surface Area of a Cube Cuboid and Cylinder  6.2.2. Surface Area of a Cone and Sphere  6.2.3. Volume of a Cube Cuboid and Cylinder  6.2.4. Volume of a Cone and Sphere  6.3. Conversion of Units  6.4. Frustum of a Cone
  7. Statistics  7.1. Introduction to Statistics  7.2. Collection of Data  7.3. Presentation of Data  7.3.1. Tabular Form  7.3.2. Graphical Form  7.3.2.1. Bar Graph  7.3.2.2. Histogram  7.3.2.3. Frequency Polygon  7.3.2.4. Ogive  7.4. Measures of Central Tendency  7.4.1. Mean Median and Mode  7.4.2. Quartiles and Percentiles  7.5. Measures of Dispersion  7.5.1. Range and Interquartile Range  7.5.2. Standard Deviation and Variance
  8. Probability  8.1. Introduction to Probability  8.2. Experimental Probability  8.3. Theoretical Probability  8.4. Probability of Simple Events  8.5. Complementary Events  8.6. Probability of Compound Events

Grade 10 → Mensuration ↓


Conversion of Units


Conversion of units is an essential skill in mathematics, not only for solving problems in everyday life but also in various fields including science, engineering, and commerce. Units are used to measure quantities and when we talk about conversion of units, we are referring to the practice of converting one measurement unit into another.

It is important to understand units and be able to convert them because different systems of measurement are used in the world. The most common systems include the metric system and the imperial system.

Metric system

The metric system, which originated from France, is the most widely used measurement system. It is based on the number 10, which makes it convenient as it aligns well with the decimal number system.

The basic units in the metric system are meters for length, grams for mass, and liters for volume. From these base units, you can get larger or smaller units by adding prefixes:

  • milli- : 1/1000 or 0.001
  • centi- : 1/100 or 0.01
  • deci- : 1/10 or 0.1
  • deca- : 10
  • hecto- : 100
  • kilo- : 1000

For example:

  • 1 meter = 1000 millimeters
  • 1 gram = 1000 milligrams
  • 1 litre = 1000 millilitres
1 meter1000 millimetres

Imperial system

The imperial system, often used in the United States, primarily consists of measurements such as inches, feet, yards, and miles for length; ounces and pounds for weight; and pints, quarts, and gallons for volume.

For example:

  • 1 foot = 12 inches
  • 1 yard = 3 feet
  • 1 mile = 5280 feet
1 yard3 Feet36 inches

Why convert units?

Conversion is required when measurements are given in different units. For example, if you have a length measurement in meters and you need it in centimeters, a conversion is needed. Similarly, it may be necessary to convert liters to milliliters or grams to kilograms depending on the need or context of the problem being solved.

Basic conversion formulas

Below are some formulas for converting between common units:

Length conversion

Metric system:

1 kilometer = 1000 meters
1 meter = 100 centimeters
1 centimeter = 10 millimeters

Imperial system:

1 mile = 1760 yards
1 yard = 3 feet
1 foot = 12 inches

Mass conversions

Metric system:

1 kilogram = 1000 grams
1 gram = 1000 milligrams

Imperial system:

1 pound = 16 ounces

Conversion example

Example 1: Length conversion

Convert 5 kilometers to meters:

Since 1 kilometer is equal to 1000 meters, you multiply:
5 km = 5 × 1000 = 5000 meters

Example 2: Volume conversion

Convert 3 liters to milliliters:

1 liter is 1000 millilitres, so:
3 liters = 3 × 1000 = 3000 milliliters

Example 3: Mass conversion

Convert 2500 grams to kilograms:

Since 1 kilogram is 1000 grams, you would divide it like this:
2500 g = 2500 / 1000 = 2.5 kilograms

2.5 Kg2500 grams

Converting between metric and imperial

Sometimes you may need to convert between the metric and imperial systems. Here are some approximate conversions:

1 inch = 2.54 centimeters
1 foot = 30.48 centimeters
1 yard = 0.9144 meters
1 mile = 1.60934 kilometers
1 pound = 0.453592 kilograms
1 ounce = 28.3495 grams

Example 4: Imperial to metric conversion

Convert 10 miles to kilometers:

1 mile is approximately 1.60934 kilometers, so:
10 miles = 10 × 1.60934 = 16.0934 kilometers

Example 5: Metric to imperial conversion

Convert 50 kilograms to pounds:

1 kilogram is approximately 2.20462 pounds, so:
50 kg = 50 × 2.20462 = 110.231 pounds

50 Kg110,231 pounds

Conclusion

Knowledge of unit conversions is vital for accurate interpretation and communication of measurements. Whether in academia, professional life, or everyday activities, these conversions allow for consistency and universality in measurements.

Practicing these conversions helps hone the skill of easily converting measurements from one system to another, ensuring accuracy and fluency when working with different units of measurement.


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Conversion of Units

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