Question

Order each set of numbers from least to greatest. 7.31,7.4,7.110,7.3,7.04,7.149

Short answer

7.04, 7.110, 7.149, 7.3, 7.31, 7.4.

Step-by-step solution

Identify the Numbers

List all the numbers you need to order: 7.31, 7.4, 7.110, 7.3, 7.04, 7.149.

Standardize Number of Decimal Places

Convert all numbers to the same number of decimal places for easy comparison. For example, 7.31 becomes 7.310, 7.4 becomes 7.400, 7.3 becomes 7.300, 7.04 becomes 7.040, while 7.110 and 7.149 remain the same.

Compare and Order the Numbers

Place the standardized numbers in ascending order: 7.040, 7.110, 7.149, 7.300, 7.310, 7.400.

Write the Original Numbers in Sorted Order

Convert the standardized numbers back to their original form and arrange them in the same order: 7.04, 7.110, 7.149, 7.3, 7.31, 7.4.

Key concepts

Comparing Decimals

When comparing decimals, the first thing to focus on is the decimal places. Begin by looking at each number from left to right.
For example, if you have 7.31 and 7.4, start by comparing the whole number part (7 in both cases).
Since the whole numbers are the same, move on to comparing the decimal part.

• Compare the tenths place first. In 7.31, the digit is 3, and in 7.4, the digit is 4.
• Since 3 is less than 4, 7.31 is less than 7.4.

If you have another decimal, say 7.04, compare tenths first. Since 0 is less than 3 or 4, 7.04 is the smallest.
If the tenths place is the same, move to the hundredths place and so on until a difference is found.

Ascending Order

Ordering numbers in ascending order means arranging them from the smallest to the largest.
For the list of numbers to be in ascending order, you should first compare their decimal values.
Looking at an example: {7.31, 7.4, 7.110, 7.3, 7.04, 7.149},

• Start by identifying the smallest decimal: 7.04
• Next, we have 7.110, followed by 7.149, 7.3, 7.31, and lastly, 7.4.

By examining each number carefully, we ensure the numbers are placed correctly from the least to greatest.

Standardizing Decimal Places

To make comparing decimals easier, it's helpful to-standardize the number of decimal places.
This means converting each number so they all have the same number of digits after the decimal.
For example, if we have the numbers 7.31, 7.4, 7.3, and 7.04, we can convert these to 7.310, 7.400, 7.300, and 7.040, respectively.

• This process allows a straightforward comparison by aligning each decimal place.
• For example, 7.310 is less than 7.400 since 310 is less than 400.

By standardizing decimal places, it becomes easier to arrange the numbers accurately in ascending order.