Question

Identify the decimal with the largest value in the following sets. 0.4,0.44,0.444 ______

Short answer

The largest decimal is 0.444.

Step-by-step solution

Understand the Problem

We need to compare three decimal numbers: 0.4, 0.44, and 0.444 to determine which one has the largest value.

Align the Decimals

Align the decimal numbers by placing the same number of digits after the decimal point for each. This will help in comparing them effectively. 0.400 0.440 0.444

Compare the Digits

Start comparing the numbers from left to right once they are aligned. - Compare the tenths place: All numbers have 4 in the tenths place. - Compare the hundredths place: - 0.400 has 0 - 0.440 has 4 - 0.444 has 4 Continue to the thousandths place: - 0.400 has no digit (or 0) - 0.440 has no digit (or 0) - 0.444 has 4

Identify the Largest Decimal

The largest decimal is the one with the highest value in the leftmost different digit column after alignment. Comparing 0.400, 0.440, and 0.444 clearly shows that 0.444 has the highest value in the thousandths place.

Key concepts

Decimal Place Values

When dealing with decimal numbers, it's important to understand that each digit has a specific value based on its position. This concept is known as 'decimal place value.' Decimal numbers are divided into parts by the decimal point. Each position to the right of the decimal point represents a fraction of ten.

• The first position is the tenths place, meaning one part in ten (e.g., 0.4 means four-tenths).
• The second position is the hundredths place (e.g., 0.04 means four-hundredths).
• The third position is the thousandths place (e.g., 0.004 means four-thousandths).

Understanding these positions helps compare and analyze decimal numbers effectively. Knowing that every increase by a position increases the precision and potential size of a decimal allows for better comparison between numbers such as 0.4, 0.44, and 0.444.

Number Alignment

The key to comparing decimal numbers effectively is proper alignment. Aligning numbers ensures that you are comparing digits within the same place value.
When listing or writing decimals for comparison, it's helpful to add trailing zeros so each number has the same number of digits after the decimal point. This doesn't change the value but makes it easier to compare them directly.
- For example, writing 0.4 as 0.400 doesn't change its value. - Similarly, 0.44 becomes 0.440. - This alignment gives a clearer visual element to recognize distinctions between decimals like 0.400, 0.440, and 0.444.

Place Value Comparison

Place value comparison involves evaluating each digit according to its significance based on its position.
When comparing decimals:

• Start from the leftmost digit, proceeding to the right, until you find a difference.
• Check the tenths, then the hundredths, and so on.

In the example of the decimals 0.400, 0.440, and 0.444, they all have 4 in the tenths place.
Next, look at the hundredths place where 0.440 and 0.444 have 4, but 0.400 has 0.
Further examination of the thousandths place shows that 0.444 has a 4, where others effectively have 0 (since no digits are present).
This methodical approach allows you to see that 0.444 is the greatest decimal thanks to its higher value at each respective place.