Rules and Tricks for Comparing and Arranging Decimals
Decimals play an important role in everyday life, specifically in terms of money. So it is important to understand how they work, and how to arrange them in proper order. Arranging the decimals numbers in order can be tricky because if we look at the numbers 2.67 and 2.409 and say 2.409 is a greater number because the number of digits is more. Then, it is completely wrong. The correct answer is 2.67.
2.67 is greater than 2.409 due to the trailing zero concepts. Trailing zeros is a zero digit in the representation of the decimal number after which no other digit follows. Therefore, we can write 2.67 as 2.670.
In this article, we will discuss what are decimal numbers and certain rules for ordering decimals that enable us to easily compare two or more decimal numbers.
What are Decimal Numbers?
Decimal numbers are the numbers in a fractional part that is written after the decimal point. The decimal point in the decimal number separates the whole number part and fractional part.
The digits lying to the left of the decimal point represent the whole number part whereas the digits lying to the right of the decimal point represent the fractional part.
The places in the whole number part begin with ones, then tens, then hundreds, then thousands, then ten thousands, and so on.
The places in the fractional number part start with tenths, then hundredths, then thousandths, then ten thousandths, and so on.
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Let us now look at the rules for ordering decimals.
Ordering Decimals Rules
Decimals numbers are either arranged in ascending order or descending order. Ordering decimals numbers is similar to ordering whole numbers. For ordering decimals, certain rules should be followed that enable us to compare two or more decimal numbers easily.
Following are the rules that should be followed while ordering decimals numbers.
To order a given number of decimals, first, arrange them vertically so that their decimal points are exactly one above the other.
Place the decimal point at the end of the number that does not have a decimal.
More digits in number do not mean that a given decimal number is greater. For example, 2.67 and 2.409.
Zero should be added to the right of the decimal number so that all the numbers have the same decimal place.
The digits with the same place value are compared starting from the left side.
The decimal number with a greater digit in the tenths place is greater. For example, 7.95 is greater than 7.85. If the digits given in one place are equal, then compare the digits in the tenths place. If the digits given in the tenths place are equal, then compare the digits in the hundredths place. The decimal number with the greater digit in the hundredths place is greater.
Let us understand these steps with an example:
Examples:
1. Which is greater 7.4 or 7.415?
Solution:
Step 1: First arrange the number vertically so that their decimal points are exactly one above the other.
7 . 4
7 . 4 1 5
Step 2: Add the digit 0 to the right of 7.4 so that both the numbers have the same decimal place.
7 . 4 0 0
7 . 4 1 5
Step 3: Start comparing the given digits from the leftmost side to determine the greater decimal number.
The digits in the ones place 7 and tenth place 4 in 7.4 and 7.46 are the same. Next, compare the digits in the hundredths place. We can see that the digit in the hundredths place is 7.415 is 1, whereas the digit in the hundredths place is 7.400 is 0. As 1 > 0.
Therefore, 7.415 > 7. 400 0r 7.415 > 7.4.
2. Which is greater 9.434 or 9.4365?
Step 1: First arrange the number vertically so that their decimal points are exactly one above the other.
9 . 4 3 4
9. 4 3 6 5
Step 2: Add the digit 0 to the right of 9.434 so that both the numbers have the same decimal place.
9 . 4 3 4 0
9. 4 3 6 5
Step 3: Start comparing the given digits from the leftmost side to determine the greater decimal number.
The digits in the ones place 7, tenth place 4 and hundredths place 3 in 9.4340 and 9.4365 are the same. Next, compare the digits in the thousandths place. We can see that the digit in the thousandths place in 9.4365 is 6 whereas the digit in the thousandths place in 9 .4340 is 4. As 6 > 4.
Therefore, 9.4365 > 9 .4340 or 9.4365 > 9 .434.
Ordering Decimals Solved Example
The Jones family drove to the nearest gasoline station. The station has three petrol pumps each marked in price per gallon. Determine which pump has the highest price per gallon.
The price per gallon of three pumps are $ 2.7, $2.96, $2 .69
Solution:
Step 1: First arrange the number vertically so that their decimal points are exactly one above the other.
2 . 7
2 . 9 6
2 . 6 1
Step 2: Add the digit 0 to the right of 2.7 so that all the three numbers have the same decimal place.
2 . 7 0
2 . 9 6
2 . 6 1
Step 3: Start comparing the given digits from the leftmost side to determine the greater price.
The digit in the ones place 2 is the same in all three numbers. Next, compare the digits in the tenths place. We can see that the digit in the tenths place in 2.60 is 6, the digit in tenths place in 2.96 is 9, and the digit in the tenth place in 2.61 is 6. As 9 > 7 > 6.
Therefore, 2.96 > 2.79 , and 2.96 > 2.61.
Hence, the gasoline pump marked with 2.96 has the highest precise per gallon.
2. Which number is greater than 419.653 or 419.651?
Solution:
First, check the whole number part of a decimal number
419 = 419
Then check the tenths place.
6 = 5
Then check the hundredths place.
5 = 5
Then check the hundredths place.
3 > 1
Therefore, 419.653 > 419.651.
Facts to Remember
When ordering and comparing decimals numbers, placing the value of a digit plays an important role. The further the greater digit to the left of the decimal number, the greater its value.
Although one-thousandth seems big, it is very small. One thousandth is a single portion of a whole unit divided into thousandths parts. One-tenth is one-hundredth time more than one-tenth.
FAQs on How to Order Decimals Easily
1. What is the easiest step-by-step method to order decimals?
The simplest way to order decimals involves a few key steps. First, write the decimal numbers in a column, ensuring all the decimal points are aligned. If the numbers have a different number of digits after the decimal point, add trailing zeros to the shorter ones so they all have the same length. Finally, compare the numbers from left to right, place value by place value, to determine their order.
2. How do you arrange decimals in ascending and descending order with an example?
Arranging decimals is about putting them in a specific sequence.
- Ascending order means arranging them from smallest to largest. For example, 0.5, 0.65, and 1.2 would be ordered as 0.5, 0.65, 1.2.
- Descending order means arranging them from largest to smallest. The same numbers in descending order would be 1.2, 0.65, 0.5.
3. What is the importance of adding trailing zeros when ordering decimals?
Adding zeros to the end of a decimal (e.g., changing 0.7 to 0.70) does not change its value but makes comparison much easier. It helps to equalise the number of decimal places across all numbers, allowing for a direct, visual comparison. For instance, to compare 0.8 and 0.75, rewriting 0.8 as 0.80 makes it immediately clear that it is larger than 0.75.
4. What is the most common mistake students make when ordering decimals?
A very common error is to ignore the decimal point and compare the digits as if they were whole numbers. For example, a student might mistakenly think 0.9 is smaller than 0.85 because 9 is less than 85. The correct approach is to compare place values, where the '9' in the tenths place of 0.9 is greater than the '8' in the tenths place of 0.85, making 0.9 the larger number.
5. Why is understanding place value the most important concept for ordering decimals?
Place value is the fundamental principle behind ordering decimals because it dictates the actual value of each digit. A digit in the tenths place (the first digit after the decimal) is ten times more valuable than a digit in the hundredths place (the second digit). Without a solid grasp of place value, it's impossible to correctly determine whether 0.4 is greater or smaller than 0.14, as you wouldn't be comparing the correct parts of the number.
6. Can you provide a real-world example of where ordering decimals is used?
Ordering decimals is a crucial skill used in many everyday situations. A great example is in sports, like swimming or running, where an athlete's time is recorded in decimals (e.g., 9.58 seconds vs. 9.63 seconds). To determine the winner, the times must be ordered from smallest (fastest) to largest. Another example is comparing the prices of items in a store, like ₹45.50 and ₹45.75, to find the cheaper product.
