Understand the concept of multiplying by 100

Oct 13, 2025 by miodeya.com 45 views

Understanding the Problem

In this problem, we are given a decimal number $0.98345$ and asked to multiply it by $100$ . The result of this multiplication will be a new decimal number. Our goal is to find the correct answer among the given options.

Why Multiply by 100?

Multiplying a decimal number by $100$ is equivalent to moving the decimal point two places to the right. This is because $100$ is equal to $10^2$ , and when we multiply a number by $10^2$ , we are essentially shifting its decimal point two places to the right.

Step-by-Step Solution

To solve this problem, we can follow these steps:

Understand the concept of multiplying by 100: As mentioned earlier, multiplying a decimal number by $100$ is equivalent to moving the decimal point two places to the right.
Apply the concept to the given number: We need to multiply $0.98345$ by $100$ . To do this, we will move the decimal point two places to the right.
Perform the multiplication: $0.98345 \times 100 = 98.345$

Analyzing the Options

Now that we have found the correct answer, let's analyze the options given:

A) 9.8345: This option is incorrect because it is missing a digit in the hundredths place.
B) 983.45: This option is incorrect because it is missing a digit in the tenths place.
C) 98.345: This option is correct because it matches our calculated answer.
D) 0.0098345: This option is incorrect because it is the result of multiplying $0.98345$ by $0.01$ (not $100$ ).

Conclusion

In conclusion, the correct answer to the problem $0.98345 \times 100 = ?$ is C) 98.345. This is because multiplying a decimal number by $100$ is equivalent to moving the decimal point two places to the right, and applying this concept to the given number yields the correct answer.

Real-World Applications

Multiplication of decimal numbers is a fundamental concept in mathematics that has numerous real-world applications. For example:

Finance: When calculating interest rates or investment returns, decimal numbers are often used to represent percentages.
Science: In scientific calculations, decimal numbers are used to represent measurements and quantities.
Engineering: In engineering applications, decimal numbers are used to represent dimensions and tolerances.

Common Mistakes

When multiplying decimal numbers, it's essential to remember the following common mistakes:

Incorrect placement of decimal points: When multiplying decimal numbers, it's easy to get the decimal point in the wrong place. Make sure to move the decimal point the correct number of places.
Forgetting to multiply the digits: When multiplying decimal numbers, don't forget to multiply the digits in each place value.

Practice Problems

To practice multiplying decimal numbers, try the following problems:

$0.56789 \times 100 = ?$
$0.12345 \times 1000 = ?$
$0.98765 \times 1000 = ?$

Conclusion

Frequently Asked Questions

In this article, we will address some of the most common questions related to multiplication of decimal numbers.

Q: What is the rule for multiplying decimal numbers?

A: The rule for multiplying decimal numbers is to multiply the numbers as if they were whole numbers, and then place the decimal point in the correct position.

Q: How do I know where to place the decimal point?

A: To determine where to place the decimal point, count the number of decimal places in the factors and add them together. The decimal point in the product will be placed that many places to the left.

Q: What if I have a decimal number with a negative exponent?

A: When multiplying a decimal number with a negative exponent, you can rewrite the exponent as a positive exponent by moving the decimal point to the right. Then, multiply the numbers as usual.

Q: Can I multiply decimal numbers with different numbers of decimal places?

A: Yes, you can multiply decimal numbers with different numbers of decimal places. To do this, first, multiply the numbers as if they were whole numbers, and then place the decimal point in the correct position.

Q: How do I multiply a decimal number by a power of 10?

A: When multiplying a decimal number by a power of 10, you can simply move the decimal point to the right by the number of places indicated by the exponent.

Q: What if I have a decimal number with a repeating decimal?

A: When multiplying a decimal number with a repeating decimal, you can use the concept of infinite geometric series to find the product.

Q: Can I use a calculator to multiply decimal numbers?

A: Yes, you can use a calculator to multiply decimal numbers. However, make sure to enter the numbers correctly and follow the order of operations.

Q: How do I check my answer when multiplying decimal numbers?

A: To check your answer when multiplying decimal numbers, you can use the following methods:

Multiply the numbers again and compare the result to your original answer.
Use a calculator to check your answer.
Round the numbers to a reasonable number of decimal places and multiply them again.

Q: What are some common mistakes to avoid when multiplying decimal numbers?

A: Some common mistakes to avoid when multiplying decimal numbers include:

Forgetting to multiply the digits in each place value.
Incorrectly placing the decimal point.
Not following the order of operations.
Not using a calculator or other tools to check your answer.

Q: How can I practice multiplying decimal numbers?

A: You can practice multiplying decimal numbers by:

Using online resources and practice problems.
Working with a partner or tutor to practice multiplying decimal numbers.
Using real-world examples and applications to practice multiplying decimal numbers.

Conclusion

In conclusion, multiplying decimal numbers is a fundamental concept in mathematics that has numerous real-world applications. By understanding the rules and concepts related to multiplication of decimal numbers, you can solve problems and make accurate calculations. Remember to avoid common mistakes and practice multiplying decimal numbers to become proficient in this skill.