Question

Order each set of numbers from least to greatest. 21.5,20.50,22.500,20.719,21.66,21.01,20.99

Short answer

20.50, 20.719, 20.99, 21.01, 21.5, 21.66, 22.500

Step-by-step solution

List the numbers

Start by writing down all the numbers in the set: 21.5, 20.50, 22.500, 20.719, 21.66, 21.01, 20.99

Compare numbers

Compare each number by looking at the value of their digits from left to right. Align them vertically by decimals for easier comparison if necessary.

Order the numbers

Begin placing the smallest number first and continue to the largest. 1. 20.50, 2. 20.719, 3. 20.99, 4. 21.01, 5. 21.5, 6. 21.66, 7. 22.500

Key concepts

comparing decimals

To order decimal numbers, you first need to understand how to compare them. Look at the digits from left to right, starting with the whole number part before the decimal point. If the whole numbers are the same, move to the digits after the decimal point.
Imagine you have these numbers: 20.50 and 20.719.
First, compare the whole numbers: 20 is equal to 20. Then, compare the decimals 50 (0.50) with 719 (0.719). Since 50 is less than 719, 20.50 is smaller than 20.719.
Always compare digit by digit. Add zeros if needed to make them the same length:
20.50 becomes 20.500
20.719 stays 20.719
Now compare: 500 is less than 719, so 20.50 < 20.719.
Practicing this will improve your confidence in comparing and ordering decimals. You can use these steps for any set of decimal numbers.

number sense

Number sense is your ability to understand, interpret, and work with numbers. When ordering numbers, it helps to have a strong number sense to quickly see which numbers are larger or smaller.
A good practice is to visualize the numbers on a number line. For instance, place 21.5, 20.50, and so on on an imaginary line. This visual aid can help you see that 20.50 comes before 20.719, and both come before 21.01.
Number sense includes understanding the size of numbers, their relationships to each other, and how they interact in different operations.
Strengthen your number sense by regularly practicing with sets of numbers, understanding their magnitude, and how small changes in one number can affect their order.

place value

Place value is about understanding the value of each digit in a number based on its position. In the decimal system, each place has a value ten times that of the place to its right.
For example, in the number 21.66, the digit '2' is in the tens place and is worth 20, the digit '1' is in the ones place and is worth 1, while '6' in the tenths place is worth 0.6, and the last '6' in the hundredths place is worth 0.06.
Knowing place value helps you to compare and order decimals. If you align the numbers by the decimal point, it becomes much easier to see which digits hold more value.
For instance:

• 21.66
• 21.5 (which is 21.50)
• 20.719

By comparing each digit in its place, you can accurately determine their order. Strong place value understanding is essential for decimal comparison and overall number sense.