Problem 49 Find each product and check each... [FREE SOLUTION]

Chapter 6: Problem 49

Find each product and check each result with a calculator. \(100 \cdot 0.779\)

Short Answer

Expert verified

The product is 77.9.

Step by step solution

Understand the Problem

We need to find the product of two numbers: 100 and 0.779. The task also involves verifying the result using a calculator.

Calculate the Product Manually

To find the product, multiply 100 by 0.779:\[ 100 \times 0.779 = 77.9 \].

Verify the Result Using a Calculator

Input the calculation into a calculator: 100 multiplied by 0.779. The calculator should display the result as 77.9. This confirms our manual calculation.

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Key Concepts

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

Verification with Calculator

When you multiply decimals manually, it's always a great idea to check the computed answer with a calculator.
This ensures accuracy, let's perform this verification here.

First, complete the manual calculation of multiplying 100 by 0.779. In our calculation, we found it to be 77.9.
Next, use a calculator. Enter "100" and select the multiplication sign, followed by "0.779".
The calculator should provide the output of 77.9, exactly matching the manual result.

This method not only builds confidence in your math skills but also helps catch any potential mistakes in your computations.

Step by Step Solution

Breaking down the problem into manageable steps is crucial for understanding decimal multiplication.
Let's revisit the provided step by step solution and make it even clearer.

Step 1: Grasp the task at hand. You need to find the product of two numbers, and importantly, one of them is a decimal. Here, it's multiplying 100 by 0.779.
Step 2: Perform the multiplication. Start by aligning the numbers vertically if doing it by hand. Here's what it looks like in this problem: 100 becomes 100.000, because we're working with a decimal. Multiply systematically. Each digit of 100 is multiplied by 0.779. 100 x 0.779 gives 77.9.
Step 3: Confirm the result. Once the manual multiplication is done, reassure yourself by using a calculator to validate that 100 times 0.779 equals 77.9.

These steps are designed to reinforce your understanding and to make sure that each component of the problem is tackled correctly.

Mathematical Understanding

Behind every math problem, there鈥檚 a web of concepts waiting to be unraveled.
It鈥檚 not just about numbers; it鈥檚 about *how* those numbers work together.

**Place Value and Decimals:** When working with decimals like 0.779, remember that each digit stands in a specific place value. Here, 7 is in the tenths, 7 arises again in the hundredths, and 9 in the thousandths position.
**Multiplying with 100:** Multiplication by 100 is essentially a mathematical shift, moving the decimal point two places to the right. It's effectively the same as multiplying any number by 10 twice.

Grasping these concepts prepares you for a broader spectrum of mathematics, enhancing both your calculating ability and your number sense.

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91影视

Find each product and check each result with a calculator. \(100 \cdot 0.779\)

Short Answer

Step by step solution

Understand the Problem

Calculate the Product Manually

Verify the Result Using a Calculator

Key Concepts

Verification with Calculator

Step by Step Solution

Mathematical Understanding

One App. One Place for Learning.

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