5. Fill In The Blanks To Complete The Table.$\[ \begin{tabular}{|l|l|} \hline $0.738 \times 1$ & $= \square$ \\ \hline $0.738 \times 10^1$ & $= \square$ \\ \hline $0.738 \times 10^2$ & $= \square$ \\ \hline $0.738 \times 10^3$ & $= \square$

Feb 27, 2025 by ADMIN 241 views

**Understanding Multiplication with Exponents: A Step-by-Step Guide**

Introduction

Multiplication with exponents is a fundamental concept in mathematics that helps us simplify complex calculations. In this article, we will explore the concept of multiplication with exponents and provide a step-by-step guide on how to fill in the blanks to complete the table.

What are Exponents?

Exponents are a shorthand way of writing repeated multiplication. For example, $2^3$ means $2$ multiplied by itself $3$ times, which is equal to $2 \times 2 \times 2 = 8$ . Exponents are used to represent the power or the exponentiation of a number.

Understanding the Table

The table provided is a simple multiplication table that involves multiplying a decimal number, $0.738$ , by powers of $10$ . The table has four rows, each representing a different power of $10$ .

$0.738 \times 1$	$= \square$
$0.738 \times 10^1$	$= \square$
$0.738 \times 10^2$	$= \square$
$0.738 \times 10^3$	$= \square$

Filling in the Blanks

To fill in the blanks, we need to multiply $0.738$ by each power of $10$ .

Step 1: Multiply 0.738 by 1

When we multiply $0.738$ by $1$ , we get the same value, which is $0.738$ .

Step 2: Multiply 0.738 by 10^1

To multiply $0.738$ by $10^1$ , we need to move the decimal point one place to the right, resulting in $7.38$ .

Step 3: Multiply 0.738 by 10^2

To multiply $0.738$ by $10^2$ , we need to move the decimal point two places to the right, resulting in $73.8$ .

Step 4: Multiply 0.738 by 10^3

To multiply $0.738$ by $10^3$ , we need to move the decimal point three places to the right, resulting in $738$ .

Conclusion

In conclusion, filling in the blanks to complete the table involves multiplying $0.738$ by each power of $10$ . By understanding the concept of exponents and following the steps outlined above, we can easily fill in the blanks and complete the table.

Tips and Tricks

When multiplying a decimal number by a power of $10$ , simply move the decimal point to the right by the number of places indicated by the exponent.
Exponents can be used to simplify complex calculations and make them easier to understand.
Practice makes perfect! The more you practice multiplying with exponents, the more comfortable you will become with the concept.

Common Mistakes to Avoid

Not moving the decimal point far enough to the right when multiplying by a power of $10$ .
Not understanding the concept of exponents and how they are used in multiplication.
Not practicing enough to become comfortable with the concept of multiplication with exponents.

Real-World Applications

Multiplication with exponents has many real-world applications, including:

Science and Engineering: Exponents are used to represent the power or the exponentiation of a number, which is essential in scientific and engineering calculations.
Finance: Exponents are used to calculate interest rates and investments.
Computer Science: Exponents are used in algorithms and data structures to represent the power or the exponentiation of a number.

Conclusion

Q: What is the difference between multiplication and exponentiation?

A: Multiplication and exponentiation are two different mathematical operations. Multiplication involves repeated addition, while exponentiation involves raising a number to a power.

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

A: To multiply a decimal number by a power of 10, simply move the decimal point to the right by the number of places indicated by the exponent. For example, to multiply 0.738 by 10^2, move the decimal point two places to the right, resulting in 73.8.

Q: What is the rule for multiplying exponents with the same base?

A: When multiplying exponents with the same base, add the exponents. For example, 2^3 × 2^4 = 2^(3+4) = 2^7.

Q: How do I simplify complex calculations using exponents?

A: Exponents can be used to simplify complex calculations by representing the power or the exponentiation of a number. For example, 2^3 × 2^4 can be simplified to 2^(3+4) = 2^7.

Q: What are some common mistakes to avoid when working with exponents?

A: Some common mistakes to avoid when working with exponents include:

Not moving the decimal point far enough to the right when multiplying by a power of 10.
Not understanding the concept of exponents and how they are used in multiplication.
Not practicing enough to become comfortable with the concept of multiplication with exponents.

Q: How do I apply multiplication with exponents in real-world situations?

A: Multiplication with exponents has many real-world applications, including:

Science and Engineering: Exponents are used to represent the power or the exponentiation of a number, which is essential in scientific and engineering calculations.
Finance: Exponents are used to calculate interest rates and investments.
Computer Science: Exponents are used in algorithms and data structures to represent the power or the exponentiation of a number.

Q: What are some tips for mastering multiplication with exponents?

A: Some tips for mastering multiplication with exponents include:

Practice, practice, practice! The more you practice multiplying with exponents, the more comfortable you will become with the concept.
Start with simple examples and gradually move on to more complex calculations.
Use real-world examples to illustrate the concept of multiplication with exponents.

Q: How do I know if I am using exponents correctly?

A: To ensure that you are using exponents correctly, follow these steps:

Read the problem carefully and understand what is being asked.
Identify the base and the exponent.
Apply the rules for multiplying exponents with the same base.
Simplify the calculation using the rules for exponents.

Q: What are some common errors to watch out for when working with exponents?

A: Some common errors to watch out for when working with exponents include:

Not understanding the concept of exponents and how they are used in multiplication.
Not moving the decimal point far enough to the right when multiplying by a power of 10.
Not practicing enough to become comfortable with the concept of multiplication with exponents.

Conclusion

In conclusion, multiplication with exponents is a fundamental concept in mathematics that helps us simplify complex calculations. By understanding the concept of exponents and following the steps outlined above, we can easily fill in the blanks and complete the table. With practice and patience, you will become comfortable with the concept of multiplication with exponents and be able to apply it in real-world situations.