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Chapter 4: Problem 19

Multiply. $$ 78.2 \times 0.01 $$

Short Answer

Expert verified
0.782

Step by step solution

01

Understand the Numbers

Let's break down the numbers first. We have 78.2 and 0.01. Multiplying by 0.01 is the same as moving the decimal point two places to the left.
02

Move the Decimal Point

Take the number 78.2 and move the decimal point two places to the left. This means the new position of the decimal point will be before 7, making the number 0.782.

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Key Concepts

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

decimal point movement
When multiplying by a decimal, understanding decimal point movement is crucial. Think of the decimal point as an anchor; it changes the value of the number based on its position. For example, if you multiply any number by 0.1, you move the decimal point one place to the left.

With our exercise, we have 78.2 multiplied by 0.01. To solve, we need to move the decimal point two places to the left since 0.01 has two decimal places. Imagine shifting the point from 78.2 leftwards through two 'jumps', resulting in the number 0.782.
multiplying decimals
Multiplying decimals might seem tricky at first, but it's simple once you get the hang of it. The key is to count the total number of decimal places in both numbers being multiplied.

For instance, when multiplying 78.2 by 0.01:
  • 78.2 has one decimal place.
  • 0.01 has two decimal places.

Adding these together, we get a total of three decimal places. We initially ignore the decimals, multiplying 782 by 1, getting 782. Finally, place the decimal point three places from the right, leading us to the correct result, 0.782.
basic arithmetic steps
Understanding the basic arithmetic steps is fundamental for solving problems like multiplication with decimals. Follow these steps:

  • Write down the numbers, ignoring the decimal points.
  • Multiply the numbers as if they were whole numbers.
  • Count the total number of decimal places in both original numbers.
  • Place the decimal point in the answer, starting from the right and moving left by the total count obtained.

By sticking to these steps, you convert what seems complex into a manageable sequence. This helps reduce mistakes and builds a solid foundation for more advanced math.
educational math instructions
Educational math instructions are critical for clarity and comprehension. When teaching, always break down the process into understandable chunks. Here鈥檚 how to explain multiplying decimals effectively:

  • Start with a clear definition of terms.
  • Use visual aids to showcase decimal point movement.
  • Provide relatable examples for practice.
  • Encourage step-by-step problem solving.

Educators should also foster an environment where students feel comfortable asking questions and making mistakes. This encourages active learning and deepens understanding of mathematical concepts.

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