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Chapter 6: Problem 46

Find each product and check each result with a calculator. \(10 \cdot 421.8842\)

Short Answer

Expert verified
The product is 4218.842, verified by calculator.

Step by step solution

01

Understanding the Problem

We need to find the product of multiplying 10 by 421.8842. This means we will multiply the number 421.8842 by 10 to find the answer.
02

Perform the Multiplication

To multiply 10 by 421.8842, we can simply move the decimal point one place to the right. So, \(421.8842 \times 10 = 4218.842\). This is because multiplying by 10 shifts the decimal one place to the right.
03

Check the Result with a Calculator

Using a calculator, input 421.8842, then multiply it by 10. Confirm that the calculator displays the result as 4218.842, verifying our calculation is correct.

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Key Concepts

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

Decimal Multiplication
Multiplying decimals might seem tricky at first, but it's all about understanding how the decimal point shifts. When you multiply any number by 10, you move the decimal point one place to the right. For example, let's consider multiplying the decimal number 421.8842 by 10.
  • Starting with 421.8842, we have the decimal point just after the first digit from the right, i.e., before the 4.
  • To multiply by 10, simply move this decimal point one space to the right.
  • This gives us 4218.842 as the product.
The beauty of decimal multiplication lies in its simplicity, where the position of the decimal plays a vital role but remains easy to manipulate!
Calculator Usage
Using a calculator ensures accuracy in arithmetic operations, especially when dealing with multiple decimal places. Calculators are a great tool for checking our manual arithmetic multiplication or decimal calculations. Here's how you can use a calculator to confirm the multiplication of 421.8842 by 10:
  • Switch your calculator on and clear any existing data.
  • Input the number directly as 421.8842 and press the multiply (*) button.
  • Then, enter the number 10 and press the equals (=) button.
  • The calculator will display 4218.842, confirming your manual computation.
With calculators, the possibility of manual errors reduces significantly, providing you with more confidence in your results!
Place Value Shift
Understanding place value is crucial when multiplying by powers of 10. This multiplication impacts the decimal point's position and not the digits themselves. Each digit holds a place value, and when multiplied by 10, these place values change. Here's what happens during such a place value shift:
  • Imagine the number as a series of digits, each having a place value based on its position relative to the decimal point.
  • Multiplying by 10 shifts every digit one place to the left, enhancing each digit's value. For example, 421.8842 becomes 4218.842.
  • It's not about the numbers changing but rather, how the shift increases their value by tenfold.
This understanding makes it easier to conceptualize why multiplying by 10 results in moving the decimal point, a straightforward but powerful arithmetic operation.

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Most popular questions from this chapter

Perform the following operations. \(9.26+\frac{1}{4} \cdot 0.81\)

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Perform each operation. $$ 72.15-26.585 $$
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