How to Order Decimals from Least to Greatest with Solved Examples
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 Ordering Decimals with Place Value and Number Line Methods
1. What does ordering decimals mean?
Ordering decimals means arranging decimal numbers from smallest to largest (ascending order) or largest to smallest (descending order) based on their value. When ordering decimals, compare digits place by place starting from the left (ones, tenths, hundredths, etc.). For example, in ascending order: 0.45, 0.5, 0.56 — here 0.45 < 0.5 < 0.56.
2. How do you order decimals from least to greatest?
To order decimals from least to greatest, compare the place values of each number starting from the left. Follow these steps:
- Write the decimals in a list.
- Add zeros if needed so all numbers have the same number of decimal places.
- Compare digits from left to right (ones, tenths, hundredths).
- Arrange them from smallest to largest.
3. How do you compare two decimal numbers?
To compare two decimals, line them up by place value and compare digits from left to right. The first place where the digits differ determines which is larger. Example: Compare 0.72 and 0.705 → Write as 0.720 and 0.705 → since 720 > 705, we get 0.72 > 0.705.
4. Why do we add zeros when ordering decimals?
We add zeros to decimals to make the same number of decimal places without changing their value. This helps compare place values correctly. For example, 0.5 can be written as 0.50 and 0.500 — they are equal. Adding zeros makes ordering decimals easier and more accurate.
5. What is the place value method for ordering decimals?
The place value method orders decimals by comparing digits in the ones, tenths, hundredths, and thousandths places. Steps include:
- Compare the whole number part first.
- If equal, compare tenths.
- If still equal, compare hundredths, and so on.
6. Can you give an example of ordering decimals?
Yes, here is an example of ordering decimals in ascending order: 2.3, 2.35, 2.305. First, write them as 2.300, 2.350, 2.305. Now compare digits: 300 < 305 < 350. So the correct order is 2.3, 2.305, 2.35.
7. How do you order decimals with different whole numbers?
When decimals have different whole numbers, compare the whole number part first. The decimal with the smaller whole number is smaller overall. Example: 4.56 and 3.98 → since 3 < 4, we know 3.98 < 4.56. Only compare decimal parts if the whole numbers are the same.
8. What is the difference between ascending and descending order of decimals?
Ascending order arranges decimals from smallest to largest, while descending order arranges them from largest to smallest. For example, for 0.9, 0.45, 0.72:
- Ascending order: 0.45, 0.72, 0.9
- Descending order: 0.9, 0.72, 0.45
9. What are common mistakes when ordering decimals?
A common mistake when ordering decimals is comparing digits without considering place value. For example, thinking 0.5 < 0.45 because 5 < 45 is incorrect. Write as 0.50 and 0.45 → since 50 > 45, we get 0.5 > 0.45. Always align decimals and compare place values carefully.
10. How do you order negative decimals?
To order negative decimals, remember that numbers further left on the number line are smaller. For negative numbers, the one with the greater absolute value is actually smaller. Example: −0.8 and −0.65 → since −0.8 < −0.65, ascending order is −0.8, −0.65. Compare them as positive numbers first, then reverse the order.
