Question

Arrange the following decimals from smallest to largest: 0.5,0.05,0.005 ______

Short answer

The decimals in order are: 0.005, 0.05, 0.5.

Step-by-step solution

Identify the Decimals

Write down the given decimals: 0.5, 0.05, and 0.005. We will be comparing these decimals to determine their order from smallest to largest.

Understand the Decimal Places

Count the number of decimal places in each number: 0.5 has 1 decimal place, 0.05 has 2 decimal places, 0.005 has 3 decimal places. More decimal places generally indicate a smaller number if they all start with similar initial numbers (specifically zeros).

Compare with Like Decimal Places

To make comparison easier, equalize the number of decimal places by rewriting the decimals: 0.5 becomes 0.500, 0.05 becomes 0.050, and 0.005 stays 0.005. This does not change their values; it just makes them easier to compare.

Rearrange the Decimals

Compare the rewritten decimals: 0.005, 0.050, 0.500. Thus, from smallest to largest, the original decimals in order are: 0.005, 0.05, 0.5.

Key concepts

Decimal Places

Decimals are numbers that have parts separated by a decimal point, where digits to the right of the point are fractional parts of ten. When comparing decimals, understanding decimal places is crucial. Decimal places indicate how precise a decimal number is and how it's divided into parts related to \(!\)1, 10, 100,\(!\) and so forth. For instance:

• 0.5 has one decimal place, and represents \(!\frac{5}{10}\)\(!\)
• 0.05 has two decimal places, representing \(!\frac{5}{100}\)\(!\)
• 0.005 has three decimal places, representing \(!\frac{5}{1000}\)\(!\)

The more decimal places a number has, the smaller the fractional part it represents, provided the leading non-zero digit is the same.

Number Order

Ordering numbers helps in organizing and analyzing data effectively. When arranging numbers, ensuring uniform decimal places often aids clarity. For decimals, more decimal places typically imply smaller absolute value, especially when initial digits are zeros.
For example:

• When aligning decimal numbers like 0.5, 0.05, 0.005 to the same digit length (e.g., 0.500, 0.050, 0.005), it becomes easier to see the order clearly.
• Comparing digit by digit further simplifies the sorting.

Thus, arranging such decimals in ascending order helps us see progression from smallest to largest.

Math Problem Solving

Problem solving in math involves identifying patterns, understanding rules, and applying logical steps to find a solution. With decimals, a strategic approach can simplify the problem-solving process. Here's a step-by-step method:

• Identify the decimals and their decimal places.
• Normalize these decimals by adding zeroes to match their decimal places without altering their value.
• Compare the equivalent decimals numerically from left to right.
• Arrange these based on the numerical sequence deduced.

This systematic approach not only solves the problem correctly but also builds a fundamental understanding of number relationships.

Educational Math Example

Educational math examples like sorting decimal numbers serve as practical applications of theoretical knowledge. They bridge abstract concepts with real-life uses, showing students the utility of learning math.
Consider this exercise of arranging 0.5, 0.05, 0.005:

• It teaches how to handle decimal values, enhancing precision with computations.
• It demonstrates organizing skills by sorting and ranking numbers.
• This kind of problem fosters critical thinking by challenging students to apply consistent logical processes.

Such examples are instrumental in building confidence and comprehension in math, encouraging students to apply the same principles to more complex scenarios.