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Chapter 1: Problem 15

Perform each operation. $$0.2 \cdot 2.5$$

Short Answer

Expert verified
The result of the multiplication of 0.2 by 2.5 is \(0.50\) or simply \(0.5\).

Step by step solution

01

Perform the multiplication

Multiply the two numbers as if they were whole numbers. Ignore the decimal points for now. 2 multiplied by 25 equals 50.
02

Place the decimal point

Count the number of digits after the decimal point in the original problem. There is one digit after the decimal in 0.2 and one digit after the decimal in 2.5, so there are a total of 2 digits that come after a decimal point. Now, starting from the right-most digit of your answer from step 1, count two places to the left and place the decimal point. This gives you the final answer.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Step-by-Step Solution
When tackling decimal multiplication problems, a step-by-step approach ensures you don't miss critical details. Let's break it down:
  • First, ignore the decimals and treat the numbers as whole numbers. Multiply them as you normally would. In our example, multiply 2 by 25.
  • Once the multiplication is complete, note the count of all digits to the right of the decimal in the numbers you started with. This count will determine where you'll place the decimal in your final answer.
  • Finally, insert the decimal in your answer using the total of decimal places you've counted in the previous step.
By following this systematic process, you simplify each stage, focusing just on one aspect at a time, making the complex process of decimal multiplication more manageable.
Decimal Placement
Understanding decimal placement is crucial in ensuring accuracy in decimal multiplication. Decimal points define the value of each digit in a number.
When combining decimals, the position of this point directly affects the outcome. Here's what to do:
  • Look at the equation鈥檚 visible numbers, not counting the commas. Note the total digits that follow the decimal points across both numbers being multiplied.
  • Knowing this total, adjust the decimal point in the product (result of multiplication). Count leftwards from the final digit in your product.
  • This number will locate the decimal in your answer, giving you precisely the right result.
Understanding this placement means every digit in your product holds the correct value, ensuring the mathematical integrity of your answer.
Arithmetic Operations
Arithmetic operations with decimals can seem tricky, but breaking them down into simpler parts helps greatly. When multiplying decimals:
  • Consider basic multiplication rules without the complications introduced by decimals.
  • Treat decimals separately by managing their placement only after calculation.
  • Check your work by simplifying鈥攎ultiply twice and manually estimate positions鈥攖o ensure the accuracy.
This practice of separating decimal handling from basic multiplication avoids early missteps. Arithmetic is all about combining these smaller methods for correct results. By focusing first on accurate simple multiplication and only then applying decimal rules, you stay organized, increasing accuracy in even the most complex decimal tasks.

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