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Compound Units

- Calculus
- Absolute Maxima and Minima
- Absolute and Conditional Convergence
- Accumulation Function
- Accumulation Problems
- Algebraic Functions
- Alternating Series
- Antiderivatives
- Application of Derivatives
- Approximating Areas
- Arc Length of a Curve
- Arithmetic Series
- Average Value of a Function
- Calculus of Parametric Curves
- Candidate Test
- Combining Differentiation Rules
- Combining Functions
- Continuity
- Continuity Over an Interval
- Convergence Tests
- Cost and Revenue
- Density and Center of Mass
- Derivative Functions
- Derivative of Exponential Function
- Derivative of Inverse Function
- Derivative of Logarithmic Functions
- Derivative of Trigonometric Functions
- Derivatives
- Derivatives and Continuity
- Derivatives and the Shape of a Graph
- Derivatives of Inverse Trigonometric Functions
- Derivatives of Polar Functions
- Derivatives of Sec, Csc and Cot
- Derivatives of Sin, Cos and Tan
- Determining Volumes by Slicing
- Direction Fields
- Disk Method
- Divergence Test
- Eliminating the Parameter
- Euler's Method
- Evaluating a Definite Integral
- Evaluation Theorem
- Exponential Functions
- Finding Limits
- Finding Limits of Specific Functions
- First Derivative Test
- Function Transformations
- General Solution of Differential Equation
- Geometric Series
- Growth Rate of Functions
- Higher-Order Derivatives
- Hydrostatic Pressure
- Hyperbolic Functions
- Implicit Differentiation Tangent Line
- Implicit Relations
- Improper Integrals
- Indefinite Integral
- Indeterminate Forms
- Initial Value Problem Differential Equations
- Integral Test
- Integrals of Exponential Functions
- Integrals of Motion
- Integrating Even and Odd Functions
- Integration Formula
- Integration Tables
- Integration Using Long Division
- Integration of Logarithmic Functions
- Integration using Inverse Trigonometric Functions
- Intermediate Value Theorem
- Inverse Trigonometric Functions
- Jump Discontinuity
- Lagrange Error Bound
- Limit Laws
- Limit of Vector Valued Function
- Limit of a Sequence
- Limits
- Limits at Infinity
- Limits of a Function
- Linear Approximations and Differentials
- Linear Differential Equation
- Linear Functions
- Logarithmic Differentiation
- Logarithmic Functions
- Logistic Differential Equation
- Maclaurin Series
- Manipulating Functions
- Maxima and Minima
- Maxima and Minima Problems
- Mean Value Theorem for Integrals
- Models for Population Growth
- Motion Along a Line
- Motion in Space
- Natural Logarithmic Function
- Net Change Theorem
- Newton's Method
- Nonhomogeneous Differential Equation
- One-Sided Limits
- Optimization Problems
- P Series
- Particle Model Motion
- Particular Solutions to Differential Equations
- Polar Coordinates
- Polar Coordinates Functions
- Polar Curves
- Population Change
- Power Series
- Ratio Test
- Removable Discontinuity
- Riemann Sum
- Rolle's Theorem
- Root Test
- Second Derivative Test
- Separable Equations
- Simpson's Rule
- Solid of Revolution
- Solutions to Differential Equations
- Surface Area of Revolution
- Symmetry of Functions
- Tangent Lines
- Taylor Polynomials
- Taylor Series
- Techniques of Integration
- The Fundamental Theorem of Calculus
- The Mean Value Theorem
- The Power Rule
- The Squeeze Theorem
- The Trapezoidal Rule
- Theorems of Continuity
- Trigonometric Substitution
- Vector Valued Function
- Vectors in Calculus
- Vectors in Space
- Washer Method
- Decision Maths
- Geometry
- 2 Dimensional Figures
- 3 Dimensional Vectors
- 3-Dimensional Figures
- Altitude
- Angles in Circles
- Arc Measures
- Area and Volume
- Area of Circles
- Area of Circular Sector
- Area of Parallelograms
- Area of Plane Figures
- Area of Rectangles
- Area of Regular Polygons
- Area of Rhombus
- Area of Trapezoid
- Area of a Kite
- Composition
- Congruence Transformations
- Congruent Triangles
- Convexity in Polygons
- Coordinate Systems
- Dilations
- Distance and Midpoints
- Equation of Circles
- Equilateral Triangles
- Figures
- Fundamentals of Geometry
- Geometric Inequalities
- Geometric Mean
- Geometric Probability
- Glide Reflections
- HL ASA and AAS
- Identity Map
- Inscribed Angles
- Isometry
- Isosceles Triangles
- Law of Cosines
- Law of Sines
- Linear Measure and Precision
- Median
- Parallel Lines Theorem
- Parallelograms
- Perpendicular Bisector
- Plane Geometry
- Polygons
- Projections
- Properties of Chords
- Proportionality Theorems
- Pythagoras Theorem
- Rectangle
- Reflection in Geometry
- Regular Polygon
- Rhombuses
- Right Triangles
- Rotations
- SSS and SAS
- Segment Length
- Similarity
- Similarity Transformations
- Special quadrilaterals
- Squares
- Surface Area of Cone
- Surface Area of Cylinder
- Surface Area of Prism
- Surface Area of Sphere
- Surface Area of a Solid
- Surface of Pyramids
- Symmetry
- Translations
- Trapezoids
- Triangle Inequalities
- Triangles
- Using Similar Polygons
- Vector Addition
- Vector Product
- Volume of Cone
- Volume of Cylinder
- Volume of Pyramid
- Volume of Solid
- Volume of Sphere
- Volume of prisms
- Mechanics Maths
- Acceleration and Time
- Acceleration and Velocity
- Angular Speed
- Assumptions
- Calculus Kinematics
- Coefficient of Friction
- Connected Particles
- Constant Acceleration
- Constant Acceleration Equations
- Converting Units
- Force as a Vector
- Kinematics
- Newton's First Law
- Newton's Law of Gravitation
- Newton's Second Law
- Newton's Third Law
- Projectiles
- Pulleys
- Resolving Forces
- Statics and Dynamics
- Tension in Strings
- Variable Acceleration
- Probability and Statistics
- Bar Graphs
- Basic Probability
- Charts and Diagrams
- Conditional Probabilities
- Continuous and Discrete Data
- Frequency, Frequency Tables and Levels of Measurement
- Independent Events Probability
- Line Graphs
- Mean Median and Mode
- Mutually Exclusive Probabilities
- Probability Rules
- Probability of Combined Events
- Quartiles and Interquartile Range
- Systematic Listing
- Pure Maths
- ASA Theorem
- Absolute Value Equations and Inequalities
- Addition and Subtraction of Rational Expressions
- Addition, Subtraction, Multiplication and Division
- Algebra
- Algebraic Fractions
- Algebraic Notation
- Algebraic Representation
- Analyzing Graphs of Polynomials
- Angle Measure
- Angles
- Angles in Polygons
- Approximation and Estimation
- Area and Circumference of a Circle
- Area and Perimeter of Quadrilaterals
- Area of Triangles
- Arithmetic Sequences
- Average Rate of Change
- Bijective Functions
- Binomial Expansion
- Binomial Theorem
- Chain Rule
- Circle Theorems
- Circles
- Circles Maths
- Combination of Functions
- Combinatorics
- Common Factors
- Common Multiples
- Completing the Square
- Completing the Squares
- Complex Numbers
- Composite Functions
- Composition of Functions
- Compound Interest
- Compound Units
- Conic Sections
- Construction and Loci
- Converting Metrics
- Convexity and Concavity
- Coordinate Geometry
- Coordinates in Four Quadrants
- Cubic Function Graph
- Cubic Polynomial Graphs
- Data transformations
- Deductive Reasoning
- Definite Integrals
- Deriving Equations
- Determinant of Inverse Matrix
- Determinants
- Differential Equations
- Differentiation
- Differentiation Rules
- Differentiation from First Principles
- Differentiation of Hyperbolic Functions
- Direct and Inverse proportions
- Disjoint and Overlapping Events
- Disproof by Counterexample
- Distance from a Point to a Line
- Divisibility Tests
- Double Angle and Half Angle Formulas
- Drawing Conclusions from Examples
- Ellipse
- Equation of Line in 3D
- Equation of a Perpendicular Bisector
- Equation of a circle
- Equations
- Equations and Identities
- Equations and Inequalities
- Estimation in Real Life
- Euclidean Algorithm
- Evaluating and Graphing Polynomials
- Even Functions
- Exponential Form of Complex Numbers
- Exponential Rules
- Exponentials and Logarithms
- Expression Math
- Expressions and Formulas
- Faces Edges and Vertices
- Factorials
- Factoring Polynomials
- Factoring Quadratic Equations
- Factorising expressions
- Factors
- Finding Maxima and Minima Using Derivatives
- Finding Rational Zeros
- Finding the Area
- Forms of Quadratic Functions
- Fractional Powers
- Fractional Ratio
- Fractions
- Fractions and Decimals
- Fractions and Factors
- Fractions in Expressions and Equations
- Fractions, Decimals and Percentages
- Function Basics
- Functional Analysis
- Functions
- Fundamental Counting Principle
- Fundamental Theorem of Algebra
- Generating Terms of a Sequence
- Geometric Sequence
- Gradient and Intercept
- Graphical Representation
- Graphing Rational Functions
- Graphing Trigonometric Functions
- Graphs
- Graphs and Differentiation
- Graphs of Common Functions
- Graphs of Exponents and Logarithms
- Graphs of Trigonometric Functions
- Greatest Common Divisor
- Growth and Decay
- Growth of Functions
- Highest Common Factor
- Hyperbolas
- Imaginary Unit and Polar Bijection
- Implicit differentiation
- Inductive Reasoning
- Inequalities Maths
- Infinite geometric series
- Injective functions
- Instantaneous Rate of Change
- Integers
- Integrating Polynomials
- Integrating Trig Functions
- Integrating e^x and 1/x
- Integration
- Integration Using Partial Fractions
- Integration by Parts
- Integration by Substitution
- Integration of Hyperbolic Functions
- Interest
- Inverse Hyperbolic Functions
- Inverse Matrices
- Inverse and Joint Variation
- Inverse functions
- Iterative Methods
- Law of Cosines in Algebra
- Law of Sines in Algebra
- Laws of Logs
- Limits of Accuracy
- Linear Expressions
- Linear Systems
- Linear Transformations of Matrices
- Location of Roots
- Logarithm Base
- Logic
- Lower and Upper Bounds
- Lowest Common Denominator
- Lowest Common Multiple
- Math formula
- Matrices
- Matrix Addition and Subtraction
- Matrix Determinant
- Matrix Multiplication
- Metric and Imperial Units
- Misleading Graphs
- Mixed Expressions
- Modulus Functions
- Modulus and Phase
- Multiples of Pi
- Multiplication and Division of Fractions
- Multiplicative Relationship
- Multiplying and Dividing Rational Expressions
- Natural Logarithm
- Natural Numbers
- Notation
- Number
- Number Line
- Number Systems
- Numerical Methods
- Odd functions
- Open Sentences and Identities
- Operation with Complex Numbers
- Operations with Decimals
- Operations with Matrices
- Operations with Polynomials
- Order of Operations
- Parabola
- Parallel Lines
- Parametric Differentiation
- Parametric Equations
- Parametric Integration
- Partial Fractions
- Pascal's Triangle
- Percentage
- Percentage Increase and Decrease
- Percentage as fraction or decimals
- Perimeter of a Triangle
- Permutations and Combinations
- Perpendicular Lines
- Points Lines and Planes
- Polynomial Graphs
- Polynomials
- Powers Roots And Radicals
- Powers and Exponents
- Powers and Roots
- Prime Factorization
- Prime Numbers
- Problem-solving Models and Strategies
- Product Rule
- Proof
- Proof and Mathematical Induction
- Proof by Contradiction
- Proof by Deduction
- Proof by Exhaustion
- Proof by Induction
- Properties of Exponents
- Proportion
- Proving an Identity
- Pythagorean Identities
- Quadratic Equations
- Quadratic Function Graphs
- Quadratic Graphs
- Quadratic functions
- Quadrilaterals
- Quotient Rule
- Radians
- Radical Functions
- Rates of Change
- Ratio
- Ratio Fractions
- Rational Exponents
- Rational Expressions
- Rational Functions
- Rational Numbers and Fractions
- Ratios as Fractions
- Real Numbers
- Reciprocal Graphs
- Recurrence Relation
- Recursion and Special Sequences
- Remainder and Factor Theorems
- Representation of Complex Numbers
- Rewriting Formulas and Equations
- Roots of Complex Numbers
- Roots of Polynomials
- Roots of Unity
- Rounding
- SAS Theorem
- SSS Theorem
- Scalar Triple Product
- Scale Drawings and Maps
- Scale Factors
- Scientific Notation
- Second Order Recurrence Relation
- Sector of a Circle
- Segment of a Circle
- Sequences
- Sequences and Series
- Series Maths
- Sets Math
- Similar Triangles
- Similar and Congruent Shapes
- Simple Interest
- Simplifying Fractions
- Simplifying Radicals
- Simultaneous Equations
- Sine and Cosine Rules
- Small Angle Approximation
- Solving Linear Equations
- Solving Linear Systems
- Solving Quadratic Equations
- Solving Radical Inequalities
- Solving Rational Equations
- Solving Simultaneous Equations Using Matrices
- Solving Systems of Inequalities
- Solving Trigonometric Equations
- Solving and Graphing Quadratic Equations
- Solving and Graphing Quadratic Inequalities
- Special Products
- Standard Form
- Standard Integrals
- Standard Unit
- Straight Line Graphs
- Substraction and addition of fractions
- Sum and Difference of Angles Formulas
- Sum of Natural Numbers
- Surds
- Surjective functions
- Tables and Graphs
- Tangent of a Circle
- The Quadratic Formula and the Discriminant
- Transformations
- Transformations of Graphs
- Translations of Trigonometric Functions
- Triangle Rules
- Triangle trigonometry
- Trigonometric Functions
- Trigonometric Functions of General Angles
- Trigonometric Identities
- Trigonometric Ratios
- Trigonometry
- Turning Points
- Types of Functions
- Types of Numbers
- Types of Triangles
- Unit Circle
- Units
- Variables in Algebra
- Vectors
- Verifying Trigonometric Identities
- Writing Equations
- Writing Linear Equations
- Statistics
- Bias in Experiments
- Binomial Distribution
- Binomial Hypothesis Test
- Bivariate Data
- Box Plots
- Categorical Data
- Categorical Variables
- Central Limit Theorem
- Chi Square Test for Goodness of Fit
- Chi Square Test for Homogeneity
- Chi Square Test for Independence
- Chi-Square Distribution
- Combining Random Variables
- Comparing Data
- Comparing Two Means Hypothesis Testing
- Conditional Probability
- Conducting a Study
- Conducting a Survey
- Conducting an Experiment
- Confidence Interval for Population Mean
- Confidence Interval for Population Proportion
- Confidence Interval for Slope of Regression Line
- Confidence Interval for the Difference of Two Means
- Confidence Intervals
- Correlation Math
- Cumulative Frequency
- Data Analysis
- Data Interpretation
- Discrete Random Variable
- Distributions
- Dot Plot
- Empirical Rule
- Errors in Hypothesis Testing
- Estimator Bias
- Events (Probability)
- Frequency Polygons
- Generalization and Conclusions
- Geometric Distribution
- Histograms
- Hypothesis Test for Correlation
- Hypothesis Test of Two Population Proportions
- Hypothesis Testing
- Inference for Distributions of Categorical Data
- Inferences in Statistics
- Large Data Set
- Least Squares Linear Regression
- Linear Interpolation
- Linear Regression
- Measures of Central Tendency
- Methods of Data Collection
- Normal Distribution
- Normal Distribution Hypothesis Test
- Normal Distribution Percentile
- Point Estimation
- Probability
- Probability Calculations
- Probability Distribution
- Probability Generating Function
- Quantitative Variables
- Quartiles
- Random Variables
- Randomized Block Design
- Residual Sum of Squares
- Residuals
- Sample Mean
- Sample Proportion
- Sampling
- Sampling Distribution
- Scatter Graphs
- Single Variable Data
- Skewness
- Standard Deviation
- Standard Normal Distribution
- Statistical Graphs
- Statistical Measures
- Stem and Leaf Graph
- Sum of Independent Random Variables
- Survey Bias
- Transforming Random Variables
- Tree Diagram
- Two Categorical Variables
- Two Quantitative Variables
- Type I Error
- Type II Error
- Types of Data in Statistics
- Venn Diagrams

I recall back in SFG, junior high dormitory, the senior prefect and bully who I had offended had asked me, "would you prefer to take a 'standard punishment' or perhaps a 'compound punishment'?" You really don't want to know what a 'standard' or 'compound' punishment is. However, hereafter, you would be learning about problems with compound units, their lists, as well as conversions between **standard and compound units**. Tighten your seat belt.

Problems of compound units are all tasks involving compound units that are not limited to but include the derivation, conversion, identification, and overall application of compound units in all fields.

If you don't get prepared for compound units, it may turn into a compound punishment, which may over time turn into a standard punishment.

Moving forward, it is indeed integral to define both compound and standard units.

A standard unit is a simple and single unit of measurement generally used for a quantity.

For example, centimetres, seconds, kilograms, centigrade, etc.

Note that it is not in combination with any other unit. So, an area measured in \(m^2\) or even a volume in \(cm^3\) is still a standard unit since only one unit which is meters or centimetres is in operation.

Compound units are units of measurement which comprise two, or more, different units.

They may be referred to in the unit as:

a combination of two, or more, standard units – such as speed measured in \(ms^{–1}\)

or as a new unit – such as force measured in newtons \((N)\).

Examples of compound units are \(ms^{–2}\), \(kgm^{–3}\), pascal \((Pa)\), joules, and watts.

Do not mistake standard units for SI units. SI units comprise both standard and compound units internationally (globally) used in measuring quantities.

Apparently, there are several compound units. Herein, the basic standard units which are indeed needed in your routine calculations will be enlisted in the table below.

Quantity | Compound unit |

speed and velocity | \[ms^{-1}\] |

acceleration and retardation | \[ms^{-2}\] |

density | \[kgm^{-3}\] |

force | \[N\] or \[kgms^{-2}\] |

work | \[J\] or \[kgm^2s^{-2}\] |

power | \[W\] or \[kgm^2s^{-3}\] |

pressure | \[Nm^{-2}\] or \[Pa\] |

molar concentration | \[moldm^{-3}\] |

Having understood the definitions and examples of standard as well as compound units, it would become less challenging to convert from standard to compound units and vice versa.

This is the most common instance in unit conversion. It involves combining two or more standard units which are different. Such combinations involve simple to complex operations of multiplication and division. Note that some could involve exponentials as well as roots.

The two most important questions to ask when making these conversions or derivations are, "what standard units are involved?" Also, "what operations are involved?" This second question is usually answered when you know the formula used in calculating the compound quantity. A compound quantity is a quantity that is derived from the combination of two or more quantities.

Determine the unit of measuring a quantity \(H\) which is a quotient of distance and time.

**Solution:**

Here, the quantity \(H\) is derived from dividing distance by time.

Step 1: Find the unit of component quantities. Component quantities are quantities that are used in deriving a compound quantity. Here, the component quantities are distance and time. The unit of distance metres, \(m\), and the unit of time is seconds, \(s\).

Step 2: Apply the operation needed. In this case, it is the quotient of distance and time. Thus, we are dividing so that \[H=\frac{m}{s}\]

Hence, the unit of the quantity, \(H\) is \(ms^{-1}\).

Work is the product of force and distance. Find the unit of work.

**Solution:**

We have been told that work is the product of force and distance.

Step 1: Find the unit of component quantities. Here, the component quantities are force and distance. The unit of force is newtons, \(N\), and the unit of distance is meters, \(m\).

Step 2: Apply the operation needed. In this case, it is the product of force and distance. Thus, we are multiplying so that if work is \(W\), then, \[W=N\times m\]

Hence, the unit of the quantity, \(W\) is \(Nm\).

This is generally known as Joules, \(J\).

Just as compound units are derived from a combination of standard units, standard units can be determined when compound units are broken by either standard or other compound units. Some examples below would elaborate better.

If the density of a material is \(5\, kgdm^{-3}\), find the mass when its volume is \(20\, dm^3\).

**Solution:**

Step 1: Look through the units given, and classify the units into compound and standard units. Note sometimes, both units may be compound units. In such cases, determine which compound unit is more complex. This is often easy to spot because the more elements in a unit, the more complex it is.

For instance, \(kgm^{-3}K^{-1}\) is more complex than \(dm^3\).

This question provides two units, a compound unit, \(kgdm^{-3}\) and a standard unit, \(dm^3\).

Step 2: Determine the relationship between both units by comparing both. Try to see differences. If the standard (or less complex compound) unit is seen to be part of the more complex unit, and it is not different in its exponentials, then, you divide. Otherwise, you should multiply both quantities. When doing this, do so with the units because you wish to determine the unit of the unknown too.

In this case, the unit \(dm^3\) which is found in \(kgdm^{-3}\) has a different exponential. Because the standard unit has an exponential of \(3\), while the compound unit has an exponential of \(-3\) for \(dm\). This suggests you are to multiply.

Step 3: Carryout the operation explicitly. Thus, \[5\, kgdm^{-3}\times 20\, dm^3=5\times20\times kg\times dm^{-3}\times dm^{3}\]

Note that \[dm^{-3}\times dm^{3}=1\]

Hence, the mass \(m\) of the material is \[m=5\times 20\times kg\times1\] This gives \[m=100\, kg\]

Notice that our answer has a unit, therefore, the unit for mass is \(kg\).

Sometimes you may need to convert from one compound unit to another. This may take place within the same unit, or it may involve an entirely different unit used to measure the same quantity.

This takes place when you wish to convert the same units which vary based on the exponential of \(10\). Exponential of \(10\) means, \(10^a\) or \(10^{-a}\), where \(a\) is \(1\), \(2\), \(3\)...\(n\).

The power produced by a machine is \(15\, kW\). Find the power of the same machine in \(MW\).

**Solution:**

Step 1: Identify the units involved. Your value has been given in kilowatts, \(kW\), while your answer is in megawatts, \(MW\).

Step 2: Define the relationship between units. If \[1\, kW=10^3\, W\] and \[1\, MW=10^6\, W\] with \[10^6=10^3\times10^3\] we can say \[1\, MW=10^3\times10^3\, W\]

Since \[1\, kW=10^3\, W\] it surely means that

\[1\, MW=10^3\times1\, kW\]

Hence,

\[1\, MW=10^3\, kW\]

or

\[1\, MW=1000\, kW\]

Step 3: So we would have to convert \(15\, kW\) to \(MW\) which is

\[15\, kW=\frac{15}{1000}\]

So our answer is \(0.015\, MW\)

Sometimes, when a quantity has more than one unit you may be required to present your answer in another compound unit.

If \[1\, Pa=7.5\times10^{-3}\, mmHg\]

and the pressure exerted on a body is \(4\, Pa\), express the pressure in \(mmHg\).

**Solution:**

Since

\[1\, Pa=7.5\times10^3\, mmHg\]

then,

\[4\, Pa=4\times7.5\times10^{-3}\, mmHg\]

So we have

\[4\, Pa=3\times10^{-2}\, mmHg\]

Essentially, rates tend to compare quantities, during such comparisons, compound units are formed. Most times, rates are ideal when it involves money or time.

Wage and salary tell us how much someone is paid over a period. This relationship is also known as wage rate or salary rate. It provides a compound unit which is usually a certain amount per time.

A man is paid \(£120\) for \(6\) hours of labour. What is his hourly wage?

**Solution:**

We intend on knowing how much he is paid for 1 hr. So, \[£120=6\, hrs\] Divide both sides by \(6\) to arrive at \[£20=1\, hr\]

Now to derive our compound unit, divide, by \(1\, hr\) to get \[£20\, hr^{-1}=1\]

The \(1\) signifies \(1\) unit of labour which is interpreted as \(1\) unit of labor at the rate of \(£20\, hr^{-1}\).

Note that the compound unit here is \(£hr^{-1}\).

The price of goods is also very relevant as compound units can be derived from it. For instance, \(£6barrel^{-1}\) of fuel, \(£2sweet^{-1}\) and so on.

More practice would increase your ability to solve questions on compound units.

Classify the following quantities in a table based on the compound and standard units; displacement, velocity, volume, area, force, pressure, electromagnetic induction, and electric current.

**Solution:**

The compound and standard units can be arranged as

Standard Units | Compound Units |

electric current | velocity |

displacement | force |

volume | pressure |

area | electromagnetic induction |

Imisi covers a distance of \(500\, m\) in \(160\, s\), find the Imisi's speed in miles per hour.

**Solution:**

We know speed is usually measured in \(ms^{-1}\), but our answer this time is to be in another compound unit that measures speed.

Step 1: Convert the related components. Here, we have two components, distance and time. So, convert the distance in meters to miles. If \[1\, m=6.2\times10^{-4}\, mi\]

Then,

\[500\, m=500\times6.2\times10^{-4}\, mi\]

\[500\, m=3.1\times10^{-1}\, mi\]

Likewise, convert seconds to hours. If

\[1\, s=2.78\times10^{-4}\, hr\]

Then,

\[160\, s=160\times2.78\times10^{-4}\, hr\]

\[160\, s=4.448\times10^{-2}\, hr\]

Step 2: Calculate the speed with new values.

\[\frac{3.1\times10^{-1}\, mi}{4.448\times10^{-2}\, hr}\]

Hence the speed in \(mihr^{-1}\) is \(7\, mihr^{-1}\).

- Problems of compound units are all tasks involving compound units that are not limited to but include the derivation, conversion, identification and overall application of compound units in all fields.
- Compound units are units of measurement which comprise two, or more, different units.
- Just as compound units are derived from a combination of standard units, standard units can be determined when compound units are broken by either standard or other compound units.
- Sometimes you may need to convert from one compound unit to another.
- Rates tend to compare quantities, during such comparisons, compound units are formed

Yes, density is a compound unit given it comprises of the quotient of mass and volume.

Compound units are units of measurement which comprise two, or more, different units.

Yes, pressure is a compound measure or compound unit since it is Force divided by area.

^{-1} and is a compound unit.

More about Compound Units

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