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Chapter 4: Problem 45

Multiply. $$ \begin{array}{r} 3.005 \\ \times 0.623 \\ \hline \end{array} $$

Short Answer

Expert verified
1.871115

Step by step solution

01

Understand the Problem

We need to multiply two decimal numbers, 3.005 and 0.623.
02

Remove Decimal Points

Convert the numbers to whole numbers to simplify the multiplication. 3.005 becomes 3005 and 0.623 becomes 623.
03

Perform Multiplication

Multiply the whole numbers: \(3005 \times 623\). This gives us 1,871,115.
04

Adjust for Decimal Places

Count the total number of decimal places in the original numbers. 3.005 has 3 decimal places and 0.623 has 3 decimal places, for a total of 6 decimal places.
05

Place the Decimal Point

Place the decimal point in the product (1,871,115) so that there are six digits to the right of the decimal point. The final result is 1.871115.

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Key Concepts

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

decimal multiplication
Decimal multiplication is similar to multiplying whole numbers but involves managing decimal points. The core idea is to convert decimals to whole numbers, multiply them, and then place the decimal point back in the correct position in the product. This ensures accuracy and maintains the decimal values in the final answer.
arithmetic operations
Arithmetic operations include addition, subtraction, multiplication, and division. When working with decimals, applying these operations involves additional steps to ensure that decimal points are correctly handled. Multiplying decimals combines basic multiplication with an understanding of how to place decimal points appropriately based on the original numbers.
mathematical steps
Understanding mathematical steps in decimal multiplication involves a structured approach:
  • First, remove the decimal points by converting decimals to whole numbers.
  • Next, perform the multiplication as you would with whole numbers.
  • Finally, adjust the decimal point in the product. This involves counting the total number of decimal places in the original numbers and ensuring that the product reflects this by having the corresponding number of decimal places.
This method ensures precision and clarity in solving decimal multiplication problems.
basic mathematics
Basic mathematics forms the foundation for more complex arithmetic operations, including decimal multiplication. Key concepts include understanding place values, how to handle decimal points, and the fundamental operations of multiplying, adding, subtracting, and dividing numbers. Mastery of these basics ensures a strong ability to tackle problems involving decimals, fractions, and other elements of arithmetic.

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Most popular questions from this chapter

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