Question

Identify the decimal with the largest value in the following sets. 1.32,1.12,1.5 ______

Short answer

1.5 is the largest decimal.

Step-by-step solution

Understand the Problem

We need to identify which decimal number is the largest from the given set: 1.32, 1.12, 1.5.

Compare Whole Number Parts

Look at the whole number part of each decimal: 1.32 (1), 1.12 (1), and 1.5 (1). All numbers have the same whole number part, 1, so we need to compare their decimal parts.

Compare Decimal Parts

Now compare the decimal parts: 1.32 has 0.32, 1.12 has 0.12, and 1.5 has 0.5. Since 0.5 is actually 0.50, which is larger than 0.32 and 0.12, we can determine that 1.5 is the largest decimal.

Verify by Conversion (Optional)

Convert the decimal parts to fractions if needed: 0.32 as 32/100, 0.12 as 12/100, and 0.5 as 50/100. Comparing fractions confirms that 0.5 (50/100) is the largest.

Key concepts

Understanding Fractions

Fractions are a way to represent a part of a whole. They consist of a numerator and a denominator, where the numerator is the top number and the denominator is the bottom number. In the context of decimals, converting a decimal to a fraction helps to understand its value better.

For instance, consider the decimal 0.32. This can be expressed as the fraction \( \frac{32}{100} \). Here, 32 is the numerator and 100 is the denominator, implying that 0.32 represents 32 parts out of 100.

When comparing decimal parts, sometimes it is easier to convert them into fractions to visually see which one has a larger numerator, as long as the denominators are the same. This method is especially helpful if the decimals have different numbers of digits after the decimal point.

• 0.32 as \( \frac{32}{100} \)
• 0.12 as \( \frac{12}{100} \)
• 0.5 as \( \frac{50}{100} \)

Converting decimals into fractions is a simple yet effective way to compare their values.

Exploring Decimal Parts

Decimal parts are crucial in determining the value of a decimal number, especially when the whole number parts are identical. After the decimal point, each digit signifies a different fraction of ten, spanning tenths, hundredths, thousandths, and so on.

For example, in the decimal 1.32:

• 1 is the whole number part
• 3 is in the tenths place, representing \( \frac{3}{10} \)
• 2 is in the hundredths place, representing \( \frac{2}{100} \)

This breakdown illustrates how each subsequent digit has a smaller fractional value. Therefore, when all whole numbers are the same, indicating no difference in their value, we must focus on these decimal parts. In our example set, all numbers have a whole part of 1.

Therefore the decimals, such as 0.32, played a key role in determining which number is largest. By understanding the positions of decimal digits, you can effectively compare the value of decimals.

Performing Number Value Comparison

Number value comparison involves evaluating each part of a number to distinguish which one holds a greater value. This is particularly relevant with decimals where digits after the decimal point can significantly alter the overall number.

When comparing decimals, first observe the whole number parts. If they are equal, like in 1.32 and 1.5, shift focus to the decimal parts. Compare them digit by digit:

• 0.32 versus 0.50: Convert 0.50 into 0.5 for a clearer comparison.
• Between 0.32 and 0.5, the first digit (after the decimal) in 0.5 (which is 5) is greater than 3 in 0.32.

Hence, 1.5 is greater than 1.32. Remember, a larger digit in the tenths place indicates a larger total value than a number with a similar hundredths place value.

This step-by-step approach ensures an accurate assessment of decimal numbers based on their entire structure, confirming the greatest number in any set.