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Chapter 4: Problem 79

Find each product. $$4.05 \times 10$$

Short Answer

Expert verified
The product of 4.05 and 10 is 40.5.

Step by step solution

01

Understanding the Problem

The exercise requires us to find the product of two numbers: 4.05 and 10. The task involves multiplication of a decimal number by a whole number.
02

Multiplication by Power of 10

When multiplying a number by 10, the decimal point moves one place to the right. For the number 4.05, we will shift the decimal point one position to the right, which will give us the new number.
03

Shift the Decimal Place

Move the decimal point in 4.05 one place to the right. This changes 4.05 into 40.5. Thus, 4.05 脳 10 = 40.5.

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Key Concepts

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

Decimal Point Movement
One of the most essential elements when working with decimal numbers is understanding how the decimal point moves during multiplication. This concept becomes especially important when multiplying by powers of 10. Moving the decimal point is often simpler and more intuitive than performing traditional multiplication. For instance, when multiplying a decimal by 10, like 4.05, we achieve this by moving the decimal one place to the right, transforming 4.05 into 40.5.
This is because multiplying by 10 increases the value of each digit by a factor of ten.
  • The first step is identifying the current position of the decimal point. In 4.05, the decimal is between the digit 4 and 0.
  • Then, shift the decimal one place to the right, resulting in the number 40.5, which is the product of 4.05 and 10.
Understanding this movement makes multiplying decimals by powers of 10 quick and effortless.
Multiplying by Powers of 10
Multiplying by powers of 10 is a special case in mathematics that simplifies many tasks due to the straightforward movement of the decimal point. When multiplying by powers of 10, the number of zeros in the power of 10 indicates how many positions the decimal point should move to the right. For instance, multiplying by 10, 100, or 1000:
  • Multiplying by 10 shifts the decimal one place to the right.
  • Multiplying by 100 shifts the decimal two places to the right.
  • Multiplying by 1000 shifts it three places to the right.
This technique greatly reduces the complexity of multiplying decimal numbers, ensuring quick and precise calculations.
Whole Number Multiplication
Understanding whole number multiplication is fundamental in mathematics, laying the groundwork for many mathematical operations. When multiplying a decimal, like 4.05, by a whole number, such as 10, the multiplication itself is simplified by treating the operation as a straightforward multiplication by a single power of 10. Here, it's vital to:
  • Recognize that whole numbers can be seen as decimals with a zero fractional part, e.g., 10 is the same as 10.0.
  • Apply multiplication principles to move the decimal point rather than traditional multiplication, which helps in practical calculations with greater accuracy.
Practicing whole number multiplication improves confidence in handling more complex mathematical calculations involving decimals.

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Most popular questions from this chapter

Write each expression using a positive exponent. $$a^{-10}$$

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Express each number in scientific notation. $$50,000,000$$

Determine whether each number is prime or composite. $$43$$

Write each fraction in simplest form. If the fraction is already in simplest form, write simplified. $$\frac{24}{5 k}$$
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