Grade 6
  1. Number System  1.1. Whole Numbers  1.1.1. Place Value and Face Value  1.1.2. Comparing and Ordering Numbers  1.1.3. Rounding Numbers  1.1.4. Properties of Whole Numbers (Associative, Commutative, Distributive)  1.2. Integers  1.2.1. Introduction to Integers  1.2.2. Addition and Subtraction of Integers  1.2.3. Multiplication and Division of Integers  1.2.4. Properties of Integer Operations  1.3. Fractions  1.3.1. Types of Fractions  1.3.2. Equivalent Fractions  1.3.3. Simplification of Fractions  1.3.4. Addition and Subtraction of Fractions  1.3.5. Multiplication and Division of Fractions  1.3.6. Comparing and Ordering Fractions  1.4. Decimals  1.4.1. Understanding Decimals  1.4.2. Conversion between Fractions and Decimals  1.4.3. Addition and Subtraction of Decimals  1.4.4. Multiplication and Division of Decimals  1.4.5. Comparing and Ordering Decimals
  2. Algebra  2.1. Basics of Algebra  2.1.1. Variables and Constants  2.1.2. Expressions and Equations  2.1.3. Algebraic Terms and Coefficients  2.2. Solving Simple Equations  2.2.1. Balancing Equations  2.2.2. Solving One-Step Equations  2.2.3. Solving Two-Step Equations  2.3. Patterns and Sequences  2.3.1. Identifying Patterns  2.3.2. Arithmetic Sequences
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Equivalent Ratios  3.1.3. Simplifying Ratios  3.2. Proportion  3.2.1. Introduction to Proportion  3.2.2. Direct and Inverse Proportions  3.3. Percentages  3.3.1. Converting Ratios to Percentages  3.3.2. Percentage Increase and Decrease  3.3.3. Discount and Profit Calculations  3.3.4. Simple Interest Calculations in Percentages in Ratio and Proportion
  4. Geometry  4.1. Basic Geometric Shapes  4.1.1. Points, Lines, and Angles  4.1.2. Types of Angles  4.1.3. Intersecting and Parallel Lines  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Properties of Triangles  4.2.3. Sum of Angles in a Triangle  4.2.4. Congruence of Triangles  4.3. Quadrilaterals  4.3.1. Types of Quadrilaterals  4.3.2. Properties of Quadrilaterals  4.4. Circles  4.4.1. Radius and Diameter  4.4.2. Circumference and Area  4.4.3. Arcs and Chords  4.4.4. Sector and Segment
  5. Mensuration  5.1. Perimeter  5.1.1. Perimeter of Simple Shapes  5.2. Area  5.2.1. Area of Rectangles and Squares  5.2.2. Area of Triangles and Parallelograms  5.2.3. Area of Composite Figures  5.2.4. Area of Trapezium  5.3. Volume  5.3.1. Volume of Cubes and Cuboids  5.3.2. Volume of Cylinders  5.3.3. Volume of Cones  5.3.4. Surface Area of Simple Solids
  6. Data Handling  6.1. Introduction to Data  6.1.1. Types of Data  6.1.2. Organizing Data  6.1.3. Frequency Distribution  6.2. Graphs and Charts  6.2.1. Bar Graphs  6.2.2. Line Graphs  6.2.3. Pictographs  6.2.4. Pie Charts  6.3. Mean, Median, and Mode  6.3.1. Calculating Mean  6.3.2. Finding Median  6.3.3. Identifying Mode  6.3.4. Range of Data in Mean, Median, and Mode
  7. Probability  7.1. Basics of Probability  7.1.1. Understanding Probability  7.1.2. Probability of Simple Events  7.1.3. Experimental and Theoretical Probability
  8. Practical Geometry  8.1. Construction of Shapes  8.1.1. Constructing Triangles  8.1.2. Constructing Quadrilaterals  8.1.3. Constructing Circles and Arcs  8.2. Symmetry  8.2.1. Line of Symmetry  8.2.2. Rotational Symmetry  8.2.3. Translational Symmetry

Grade 6 → Number System ↓


Decimals


Decimals are an essential part of math, especially when it comes to dealing with numbers that are not whole. They are often used in many different ways in real life, including money, measurements, and data. In this lesson, we will dive deeper into understanding what decimals are, how they work, and how you can use them effectively in a variety of mathematical operations.

What is a decimal?

Decimals are a way of representing fractions. In a more technical sense, decimals are a part of the base-10 number system. The base-10 system is something we use every day - it's the ordinary numbers we use for counting and arithmetic. Decimals allow us to represent numbers that are between whole numbers.

For example:

1.5, 2.75, 0.003

All these numbers include a decimal point that separates the whole number from the fractional part. The number before the point is called the "whole number" and the number after the point is called the "fractional part" or "decimal part."

Understanding place values in decimals

The place value system is essential to understanding decimals. Each digit in a number has a position, called its place value, which determines its value. For example, in whole numbers, the place values are units, tens, hundreds, etc. In decimals, the place value extends to tenths, hundredths, thousandths, and more to the right of the decimal point.

For the number 23.456:

- '2' is in the tens place.
- '3' is in units place.
- '4' is in the tenth place.
- '5' is in the hundredth place.
- '6' is in the thousandth place.

23.456 Tens people Tenth Hundred thousandth

Converting fractions to decimals

A common way to understand decimals is to convert fractions to decimals. To convert a fraction to a decimal, you divide the numerator (the top number) by the denominator (the bottom number).

Example: 1/2 = 0.5 3/4 = 0.75 1/5 = 0.2

Adding and subtracting decimals

Adding and subtracting decimals is very similar to adding and subtracting whole numbers, except you have to make sure to align the decimal points.

Here is a step-by-step process for adding decimals:

Example: Add 3.52 and 2.3 1. Align the numbers by the decimal point: 3.52 + 2.30 ------- 2. Add them as you would whole numbers, and keep the decimal point aligned: 3.52 + 2.30 ------- 5.82

Multiplying decimals

Multiplying decimals requires an understanding of place value, but it's not much different from multiplying whole numbers. Here's how you multiply decimals:

  1. Ignore the decimal points and multiply the numbers as if they were whole numbers.
  2. Count the total number of decimal places in both original numbers.
  3. Insert a decimal point in the product (result) so that it has the same number of decimal places.
Example: Multiply 2.5 by 0.3 1. Ignore the decimal and multiply 25 by 3: 25 x 3 = 75 2. Count the total number of decimal places: 2.5 has 1 decimal place, and 0.3 has 1 decimal place. 3. Place the decimal in 75 to have 2 decimal places: Answer = 0.75

Dividing decimals

Dividing decimals may seem a little more complicated than other operations, but it follows systematic steps:

  1. Move the decimal point in the divisor to the right until it becomes a whole number.
  2. Move the decimal point in the dividend the same number of places to the right.
  3. Divide as usual, and place the decimal point directly above its place in the dividend.
Example: Divide 0.96 by 0.4 1. Move the decimal point in 0.4 one place to the right to make it a whole number: 4. 2. Move the decimal point in 0.96 one place to the right: 9.6 3. Divide as usual: 9.6 ÷ 4 = 2.4 Answer = 2.4

Decimal rounding

Rounding a decimal is a way to simplify a decimal number by reducing the number of its decimal places. It is often used when exact numbers are unnecessary or cumbersome.

Here is how to round off a decimal:

  1. Identify to which decimal place you need to round.
  2. Look at the number just to the right of that spot.
  3. If that digit is 5 or greater, add 1 to the identified position and discard all digits to the right of it. If it is less than 5, discard all digits to the right without adding.
Example: Round 3.786 to two decimal places. 1. The second decimal place is 8, and the digit to the right is 6. 2. Since 6 is greater than 5, add 1 to 8: 3.78 + 0.01 = 3.79 Answer = 3.79

Common uses of decimals

Decimals are used extensively in various fields and in everyday life. Here are some areas:

  • Money: Amounts are often expressed in decimals, such as $3.50, where .50 represents cents.
  • Measurement: Length is usually in decimals, such as 2.54 cm.
  • Statistics: Average scores and other statistics use decimals to show precision, such as 4.76 stars.
  • Data: Computers often use decimals to represent data values precisely.

Conclusion

Decimals are a fundamental part of math that lets us represent and work with numbers that aren't whole. Through understanding decimal places, performing arithmetic operations such as addition, subtraction, multiplication, and division, and learning how to convert fractions to decimals, you'll be able to handle decimals effectively in mathematical problems and real-world situations. Keep practicing, and you'll find that working with decimals becomes more natural over time.


Grade 6 → 1.4


U
username
0%
completed in Grade 6

← Prev (1.3.6)
Comparing and Ordering Fractions
Next (1.4.1) →
Understanding Decimals

Comments 



Decimals

https://www.buddymath.com/g6/1.4?bmal=en