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Chapter 4: Problem 90

Evaluate. $$ 10,000(36.94) $$

Short Answer

Expert verified
369400

Step by step solution

01

- Understand the multiplication

Recognize that you need to multiply 10,000 by 36.94.
02

- Break down the numbers

Note that multiplying by 10,000 essentially shifts the decimal point of the other number four places to the right.
03

- Perform the multiplication

Move the decimal point in 36.94 four places to the right: 36.94 becomes 369400.
04

- Write the final result

After shifting the decimal point, you get the final result: 369400.

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Key Concepts

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

Decimal Point Shift
Understanding how to shift the decimal point is crucial for multiplication with large numbers. When you multiply a number by a power of 10 (like 10, 100, 1000, etc.), you simply move the decimal point to the right. Each zero in the power of 10 represents one shift to the right. For example, multiplying by 10 shifts the decimal one place, multiplying by 100 shifts it two places, and so on.
Large Number Multiplication
When dealing with large numbers in multiplication, the decimal point shift becomes very handy and simplifies the process. In the given example, multiplying 36.94 by 10,000 means you need to shift the decimal point four places to the right. Here's how it's done step-by-step:
  • Start with the original number: 36.94

  • Shift the decimal one place to the right: 369.4

  • Shift two places: 3694.

  • Shift three places: 36940.

  • Finally, shift four places: 369400
This method reduces the complexity of dealing directly with large numbers.
Basic Arithmetic
Basic arithmetic skills form the foundation for understanding and performing operations like multiplication. Multiplying by powers of ten involves simple arithmetic but can have a big payoff. For instance:
  • If you know that multiplying by 10 is the same as adding a zero to the end of a number, then multiplying by 100 is like adding two zeros.

  • This kind of basic understanding makes more complex calculations, like shifting the decimal in 36.94, straightforward.
In math, building on these simple rules helps you tackle a wide range of problems confidently.
Remember, practice makes perfect!

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Most popular questions from this chapter

The special product $$ (x+y)(x-y)=x^{2}-y^{2} $$ can be used to perform some multiplication problems. Here are two examples. $$ \begin{aligned} 51 \times 49 &=(50+1)(50-1) \\ &=50^{2}-1^{2} \\ &=2500-1 \\ &=2499 \end{aligned} \quad | \begin{aligned} 102 \times 98 &=(100+2)(100-2) \\ &=100^{2}-2^{2} \\ &=10,000-4 \\ &=9996 \end{aligned} $$ Once these patterns are recognized, multiplications of this type can be done mentally. Use this method to calculate each product mentally. $$ 30 \frac{1}{3} \times 29 \frac{2}{3} $$

Find each product. $$ (2 m+5)(2 m-5) $$

Evaluate each expression for \(x=3 .\) See Sections 1.3 and 1.6. $$ 3 x^{2}-3 x+4 $$

Find each product. $$ \left(\frac{3}{4}-x\right)\left(\frac{3}{4}+x\right) $$

Evaluate. $$ 49 \div 10,000 $$
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