Grade 7
  1. Number System  1.1. Integers  1.1.1. Properties of Integers  1.1.2. Operations on Integers  1.1.3. Additive and Multiplicative Inverses  1.1.4. Applications of Integers  1.2. Rational Numbers  1.2.1. Definition of Rational Numbers  1.2.2. Properties of Rational Numbers  1.2.3. Operations on Rational Numbers  1.2.4. Standard Form of Rational Numbers  1.3. Decimals  1.3.1. Operations on Decimals  1.3.2. Converting Between Fractions and Decimals  1.4. Powers and Exponents  1.4.1. Laws of Exponents  1.4.2. Simplifying Expressions with Exponents  1.4.3. Scientific Notation  1.5. Roots  1.5.1. Square Roots  1.5.2. Cube Roots
  2. Algebra  2.1. Expressions  2.1.1. Algebraic Expressions  2.1.2. Simplifying Expressions  2.1.3. Evaluating Expressions  2.2. Linear Equations  2.2.1. Solving Simple Equations  2.2.2. Applications of Linear Equations  2.3. Algebraic Identities  2.3.1. Expanding Using Identities  2.3.2. Simplifying Using Identities
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Simplifying Ratios  3.1.3. Equivalent Ratios  3.2. Proportion  3.2.1. Concept of Proportion  3.2.2. Direct Proportion  3.2.3. Inverse Proportion  3.3. Unitary Method  3.3.1. Solving Problems Using the Unitary Method
  4. Geometry  4.1. Lines and Angles  4.1.1. Types of Angles  4.1.2. Pairs of Angles  4.1.3. Properties of Parallel Lines and a Transversal  4.1.4. Angle Bisectors  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Angle Sum Property  4.2.3. Exterior Angle Property  4.2.4. Pythagoras Theorem  4.3. Congruence of Triangles  4.3.1. Criteria for Congruence  4.3.2. Applications of Congruence  4.4. Quadrilaterals  4.4.1. Types of Quadrilaterals  4.4.2. Properties of Parallelograms  4.4.3. Special Quadrilaterals  4.4.4. Properties of Rectangles and Rhombuses
  5. Mensuration  5.1. Perimeter and Area  5.1.1. Perimeter of Plane Figures  5.1.2. Area of Plane Figures  5.1.3. Area of a Trapezium  5.1.4. Area of a Parallelogram  5.1.5. Area of a Circle  5.1.6. Area of Composite Figures  5.2. Surface Area and Volume  5.2.1. Cubes and Cuboids  5.2.2. Surface Area of Cylinders  5.2.3. Volume of Prisms and Cylinders  5.2.4. Volume and Surface Area of Cones
  6. Data Handling  6.1. Data Collection  6.1.1. Organizing Data  6.1.2. Frequency Distribution  6.2. Graphical Representation of Data  6.2.1. Bar Graphs  6.2.2. Double Bar Graphs  6.2.3. Pie Charts  6.2.4. Histograms  6.2.5. Line Graphs  6.3. Probability  6.3.1. Simple Events  6.3.2. Experimental Probability  6.3.3. Theoretical Probability
  7. Practical Geometry  7.1. Construction of Triangles  7.1.1. Constructing Triangles Given Side Lengths  7.1.2. Constructing Triangles Given Side and Angle  7.1.3. Constructing Right-Angled Triangles  7.2. Construction of Quadrilaterals  7.2.1. Quadrilaterals Given Side Lengths and Angles  7.2.2. Constructing Parallelograms and Rectangles

Grade 7 → Number System → Decimals ↓


Converting Between Fractions and Decimals


Fractions and decimals are two different ways of representing parts of a whole. Both are used frequently in math and everyday life. In classes like Grade 7, understanding how to convert between these two formats is an essential skill. Here, we'll explore how you can convert fractions to decimals and decimals to fractions, with plenty of examples to illustrate the process.

What is fraction?

A fraction is a way of representing a number that is smaller than a whole number. It consists of two parts:

numerator/denominator

The numerator is the top number and it shows how many parts we have. The denominator is the bottom number and it shows how many parts there are in a whole.

For example, the fraction 3/4 has a numerator of 3 and a denominator of 4. This means we have 3 parts out of a total of 4.

What is a decimal?

Decimal is another way of representing a number. It is based on powers of ten. Decimals use a decimal point to separate the whole number part from the fractional part. For example, 0.75 is a decimal number where 0 is the whole number part, and 75 is the fractional part.

The place values for decimal numbers from left to right are as follows:

tenths, hundredths, thousandths, etc.

Converting fractions to decimals

To convert a fraction to a decimal the numerator needs to be divided by the denominator. This can be done using long division. Here is a step-by-step guide:

Step-by-step example: Convert 3/4 to a decimal

Let's convert the fraction 3/4 to decimal:

1. Write 3 divided by 4 as a division problem. 
2. 3 ÷ 4 = ? 
3. Since 3 is smaller than 4, we add a decimal point and a zero, making it 30. 
4. Divide 30 by 4. This gives us 7, with a remainder of 2. So, 7 goes after the decimal point. 
5. Bring down another zero, making it 20, then divide by 4. 
6. 20 divided by 4 is 5, with no remainder. 
7. The decimal answer is 0.75.

Visual example

Fraction: 3/4 Decimal: 0.75

Converting decimals to fractions

To convert a decimal to a fraction, follow these steps:

Converting 0.75 to a fraction

Let's convert the decimal 0.75 to a fraction:

1. Write down the decimal divided by 1. 
2. 0.75/1 
3. Multiply the numerator and the denominator by 100 to get rid of the decimal. (This is because 0.75 is in the hundredths place.) 
4. 0.75 * 100 / 1 * 100 = 75/100 
5. Simplify the fraction by finding the greatest common divisor (GCD) of 75 and 100, which is 25. 
6. Divide the numerator and the denominator by their GCD. 
7. 75 ÷ 25 / 100 ÷ 25 = 3/4

Visual example

Decimal: 0.75 Fraction: 3/4

More examples

Example 1: Convert 1/8 to decimal

1. 1 ÷ 8 = 0.125 
2. So, the fraction 1/8 is equal to the decimal 0.125.

Example 2: Convert 0.6 to a fraction

1. 0.6/1 
2. 0.6 is in the tenths place, multiply numerator and denominator by 10. 
3. 0.6 * 10 / 1 * 10 = 6/10 
4. Simplifying 6/10 gives us 3/5.

A few things to remember

  • Repeating decimals: Not all decimals end in 3. Some have a repeating pattern. For example, 1/3 = 0.333..., which has 3 repeating.
  • Terminating decimals: These decimals have an ending, such as 0.25 or 0.5.
  • Sometimes, it is useful to recognize common fraction to decimal conversions, such as 1/2 = 0.5, 1/4 = 0.25, and 3/4 = 0.75.

Practice problems

  1. Convert the fraction 5/8 to a decimal.
  2. Convert the decimal 0.875 to a fraction.
  3. Convert the fraction 7/10 to a decimal.
  4. Convert the decimal 0.2 to a fraction.

To solve these problems, use the methods and steps described above for converting between fractions and decimals.

Conclusion

Converting between fractions and decimals is a basic skill in math, helping you understand and compare quantities in different forms. It involves basic division and multiplication operations performed with careful detail, especially when it comes to repeating decimals or simplifying fractions. Practicing these conversions will increase your math fluency and make it easier to solve more complex mathematical problems in the future.


Grade 7 → 1.3.2


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Converting Between Fractions and Decimals

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