Question

Arrange the following decimals from smallest to largest: 0.123,0.1023,1.23 ______

Short answer

0.1023, 0.123, 1.23

Step-by-step solution

Understand the Question

We are given three decimal numbers (0.123, 0.1023, and 1.23) and need to arrange them from the smallest to the largest. We will compare the numbers based on their decimal value.

Compare Whole and Decimal Parts

Start by comparing the whole number part of each decimal. For 0.123 and 0.1023, the whole number part is 0. For 1.23, the whole number part is 1. Since 0 is less than 1, 0.123 and 0.1023 are smaller than 1.23.

Compare Smaller Decimals

Next, compare the decimals with whole number part 0: 0.123 and 0.1023. Compare each corresponding digit after the decimal point. The number 0.1023 has a 0 in the second decimal place, which makes it smaller than 0.123.

Arrange the Decimals

Based on the comparisons, arrange the numbers from smallest to largest: 0.1023, 0.123, 1.23.

Key concepts

Number Arrangement

Arranging numbers in a particular order, like arranging decimals from smallest to largest, is an important skill. In the context of decimals, number arrangement helps in understanding the value of numbers relative to each other. This skill is not only useful in mathematics but also in daily life applications such as budgeting and measuring.
Understanding decimal numbers begins with comparing them logically. We often arrange numbers to make decisions or evaluations easier, like ranking sizes, determining priorities, or finding the best option in a given scenario.
To arrange decimal numbers, follow these simple steps:

• Identify the whole number parts first, since they determine the order significantly when they differ.
• When whole numbers are the same, scrutinize every digit after the decimal point, comparing them systematically from left to right.
• The arrangement reflects increasing or decreasing sequences depending on what's required.

In our exercise, arranging 0.123, 0.1023, and 1.23 involves comparing first the whole numbers, and then examining decimal parts closely to determine the complete order, from the smallest to the largest.

Mathematics Education

Teaching students to understand and manipulate decimals is a foundational aspect of mathematics education. This understanding paves the way for higher-level maths concepts and real-world applications.
Decimals are integral in various streams such as algebra, geometry, and statistics. They often help to solve practical problems involving measurements, currency, and data analysis.
Effective mathematics education incorporates teaching students:

• Clear understanding of decimals and their components.
• Skills for arranging and comparing numbers systematically.
• Application of comparative techniques to real-life scenarios.

By understanding decimal comparison through exercises like arranging numbers, learners build their numeracy, which is essential for understanding more complex math topics in the curriculum. Encouraging practice with exercises similar to the one provided can solidify a student's understanding and provide confidence in handling decimals.

Place Value

Place value is a fundamental concept in mathematics that describes the value of a digit based on its position within a number. In decimals, understanding place value is even more crucial, as it determines the value of digits beyond the decimal point.
The place value system works as follows:

• Each digit in a decimal number is placed in a specific column relative to the decimal point: tenths, hundredths, thousandths, etc.
• A digit's position directly impacts its value. For example, in 0.123, the '1' is in the tenths place, making it worth 0.1.
• The further right a digit is, the smaller its value becomes, influencing the number's overall value.

Applying an understanding of place value, students can accurately compare and order decimals. The exercise of arranging the numbers 0.123, 0.1023, and 1.23, showcases how digits' positions affect their value and ultimately help in determining the arrangement of numbers from smallest to largest.