Decimals on Number Line

A decimal number line shows decimal increments and helps to identify and locate decimals accurately.

Decimals represent parts of a whole and indicate values between whole numbers, such as tenths (0.1), hundredths (0.01), and thousandths (0.001).

The number line can be partitioned into equal sections to measure decimal values. On a number line, negative values are on the left of 0, and positive values are on the right of 0. Let us see how to represent the decimals on a number line with some examples.

Representing 0.5 on a number line

Step 1: 0.5 is equidistant between 0 and 1.

Step 2: Divide the segment between 0 and 1 into 10 equal parts, each representing one-tenth(0.1).

Step 3: The 5th mark on the number line from 0 represents 0.5.

Representing 0.75 on a number line

Step 1: 0.75 is three-quarters of the way from 0 to 1.

Step 2: Divide the segment between 0 and 1 into four equal parts.

Step 3: The third mark from 0 represents 0.75.

The number line for negative decimals is similar to that for positive decimals. Negative decimals are found on the left side of the number line.  When we have negative numbers, we place them at their distance from 0, going to the left. Let us see how we can place negative decimals on the number line.

Representing -0.5 on a number line

Step 1: -0.5 is the midpoint of 0 and -1.

Step 2: To visualize it, split the number line into 10 equal parts from 0 to -1.

Step 3: The 5th mark represents -0.5.

Representing -2.3 on a number line

Step 1: - 2.3 is between - 2 and - 3.

Step 2: Divide the number line into 10 equal parts. Each part represents one-tenth(0.1).

Step 3: From -2, moving to the left, the 3rd mark is - 2.3.

Here are some tips and tricks to master decimals on number line. It helps learners to learn the subject easily.
 

1. Understand that each decimal place value represents a fraction of 1. Always observe which decimal place you are working on.
    
2. Divide the space between whole numbers into 10 equal parts for tenths, 100 for hundredths, etc. This helps in ensuring the accurate placements of decimals like 0.3, 0.75, etc.
    
3. Whole numbers and halves (0.5, 1.5, 2.5…) are easy reference points. Try to estimate decimal positions relative to these benchmarks to avoid mistakes.
             
4.  Practice comparing two decimals by placing them on a number line to see which one is bigger or smaller. The number located further to the right is always greater.
    
5. After placing the decimal, check if the position makes sense relative to the nearest whole number. For example, 0.82 should be just before 1 and not past it.
    

Decimals appear in many daily life situations, and understanding their position on a number line helps in practical tasks. Here are some of the applications.

• Money and financial transactions: Decimal numbers are crucial for transactional money needs such as prices, taxes, and discounts. Most prices are written in decimals, e.g., $9.99, $4.09, or $12.90. For example, $4.90 is between $4 and $5.
   
• Temperature readings: Decimal values are used to represent the temperature readings. For example, the exact temperatures are shown with decimals such as 23.6°C, 5.4°C, and 7.90°C. A reading of 23.6°C indicates the temperature is slightly above 23°C.
   
• Time calculation: Decimal numbers are useful in measuring time. For example, 1.5 hours means 1 hour and 30 minutes. When we represent the time 1.5 hours on the number line, it lies between 1 and 2 hours. This makes the estimation of time easier to calculate.
   
• Measuring distances: Decimals numbers are used while measuring distances for accuracy. You can measure a table that is 1.75 meters long precisely with the help of decimal numbers.
   
• Cooking and recipes: We need the perfect amount of recipes in order to make a perfect dish. If a recipe calls for 0.75 liters of milk, using 1 liter would change the taste of the dish. We can mark 0.75 on the vessel we use to pour milk.