A number line is a picture of a graduated straight line that serves as an abstraction for real numbers in elementary mathematics. Every point on a number line is assumed to correspond to a real number, and every real number is assumed to correspond to a point.
Integers are frequently depicted as specially marked points evenly spaced on a line. The line includes all real numbers, which continue indefinitely in each direction, as well as numbers that are between the integers. It is frequently used to aid in teaching simple addition and subtraction, particularly with negative numbers.
Decimal numeral system
The decimal number system (also known as the base-ten positional numeral system and denar) is the most commonly used to represent integer and non-integer numbers. It is Hindu–Arabic numeral system’s extension to non-integer numbers. Decimal notation refers to the method of denoting numbers in the decimal system. Decimals are used in situations where more precision is required in comparison to the whole numbers
E.g., When we divide 100 dollars among 40 children, we cannot use whole numbers to represent the result of the division because the fraction of share, 2.5, falls between 2 and 3. The concept of decimal was introduced to deal with similar other systems.
Dividing decimals on the number line
A decimal is a type of fraction in which the whole number is separated from the fractional part by a dot. Except for the representation method, decimals on a number line are very similar to fractions on a number line. Decimals aid us inaccurate calculations where minor differences in values are critical. In the Number system, every real number can be represented in the form of a decimal. Here, we will learn more about the representation of decimals on a number line.
All real numbers are represented on a number line. A basic unit of length is chosen as a decimal on the number line, and successive intervals of this length measure the corresponding numbers. While dividing decimals on a number line, the larger the number, the further we move to the right from the origin. Moving to the left of the origin represents negative numbers. In general, a basic unit of length is chosen in each number line that measures one unit. Consecutive intervals denote this length. These marks are then numbered as follows:
+1,+2,+3,+1,+2,+3, etc. on the right side (upper side) of the origin and as −1,−2,−3,−1,−2,−3, etc. on the left side of the origin.
A basic unit of length that includes some consecutive numbers can be chosen to present large numbers in a number line. Assume the absolute difference between the largest and smallest number in that basic length is k. Subsequent length intervals from the origin are then marked as the n-multiple of k. Wherein the right side of the origin n=1,2,3, etc. Left side is denoted as -1,-2,-3 e.t.c.
For example, suppose a basic length is chosen on the number line, which includes 10 successive numbers, i.e., the basic length measures 10 units. If we need to mark the number 50 in this number line, we must mark the point on the right side of the origin at a distance from the origin five times the basic length chosen. If we need to mark –20, we must find the distance from the origin on the left side two times the basic length.
Representation of fractions and decimals on a number line
|To represent fractions and decimals on a number line, divide each segment of the number line into ten equal parts.|
E.g. To represent 8.4 on a number line, divide the segment between 8 and 9 into ten equal parts.
The arrow is four parts to the right of 8 where it points at 8.4.
Likewise, to represent 8.45 on a number line, divide the segment between 8.4 and 8.5 into ten equal parts.
The arrow is five parts to the right of 8.4 where it points at 8.45.
Decimal fractions Decimal fractions (also recognized as decimal numbers in contexts involving explicit fractions) are rational numbers that can be expressed as a fraction with a denominator that is a power of 10.
E.g. : 0.5 decimal = 5/10, 5.3 = 53/10 , 19.86 = 1986/100 etc.
More generally, a decimal with n digits after the separator (a point or comma) represents the fraction with denominator 10n, whose numerator is the integer obtained by removing the separator.
It follows that a number is a decimal fraction if and only if it has a finite decimal representation.
Decimals on Number Line Worksheets
Decimals on a number line worksheet will assist students in understanding calculations involving decimals. A number line is a straight line in mathematics that aids in the representation of numbers.
Benefits of Decimals on Number Line Worksheets
- There are enough practice problems with decimals on a number line worksheet to understand the representation of the number decimals. Students will learn how to divide a line segment into ten equal parts to represent a decimal just on a real scale.
- These math worksheets are simple to understand and contain various questions presented in an easy-to-follow format with simplistic and exact instructions.
- The decimal on a number line worksheet can be very beneficial in developing numerical fluency, which will help learners in their higher arithmetic studies. These worksheets are planned to be interactive, and students will be able to connect the decimal calculations to real-world scenarios.
How to represent decimals on a number line?
The representation of decimals on a number line is very similar to fractions. On a number line, the negative region is defined by the left side of 0, and the positive region is represented by the right side of 0. Let us plot 0.5 and 1.4 on a number line using the steps below.
- Draw a number line by marking 0 as the reference point
- Identify and determine the integers between which the decimal lies and mark them. 0.5 lies between 0 and 1
- Similarly, 1.4 lies between 1 & 4
- Now make 10 divisions between the integers 0 and 1, 10 more between 1 and 2
- We move towards the right, starting from 0 by the number of steps equivalent to the right-most digit value after the decimal point. For 0.5, we will be moving five places towards the right of 0.
- Similarly, 1.4 would be 14 points towards the right of 0
Representation of Negative Decimals on Number Line
We use the same set of rules as described above to represent negative decimals on a number line. The only difference is that because we are dealing with negative numbers, the overall operation will be performed to the left of the origin, i.e. 0 on the number line.
Homework decimals on the number line
Q.1.To plot positive decimals on a number line, we move towards the _____ on the number line.
Q.2.To plot 0.7 on a number line, how many jumps should be made starting from 0 if there are 10 equal divisions between 0 and 1?
Q.3.To plot 1.8 on a number line, how many jumps should be made starting from 0 if there are 10 equal divisions between 0 and 2?
Q.4.To plot 2.1 on a number line, how many jumps should be made starting from 0 if there are 10 equal divisions between 0 and 3?
Multiplication of Positive Numbers on Number Line
There is a simple rule to follow when multiplying two or more positive numbers, as it purely follows simple multiplication. We’ll move to the right side of the number line since this is multiplication.
Example: Let us begin by resolving 5 x 4. Five groups of four equal intervals must be formed on the number line starting from zero. This way, we’ll be able to reach 20 people while forming five separate groups.
Multiplication of Negative Numbers on Number Line
When multiplying more than two negative numbers, use the Even-Odd Rule: count the number of negative signs. The result is positive when there are an even number of negatives but negative when there are an odd number of negatives.
Consider the following example. 10 groups of three equal intervals must be formed on the number line starting from zero. This way, we’ll get to 30 and form 10 different groups. However, due to the negative sign with 3, the groups will form to the left of the number line.
If both the numbers are negative, the result will be positive only, such as (-10) × (-3) = 30.