Problem 268
Question
In the following exercises, multiply. $$ (99.4)(1000) $$
Step-by-Step Solution
Verified Answer
99400.0
1Step 1: Understand the problem
The exercise requires multiplying two numbers: 99.4 and 1000.
2Step 2: Set up the multiplication
Write the numbers to be multiplied clearly: \[ 99.4 \times 1000 \]
3Step 3: Perform the multiplication
Multiply the whole number part first and then consider the decimal place. \[ 99.4 \times 1000 = 994 \times 100 = 99400 \]
4Step 4: Adjust for the decimal point
Since there is one digit after the decimal in 99.4, move the decimal place one position to the right in the product. \[ 99400 \rightarrow 99400.0 \]
Key Concepts
Decimal MultiplicationBasic ArithmeticStep-by-Step Math Solutions
Decimal Multiplication
Multiplying decimals may seem tricky at first, but it becomes easier with practice. Understanding how decimals work is crucial.
A key point to remember is that multiplying by 10, 100, 1000, etc. shifts the decimal point to the right.
For example, in our exercise problem, multiplying 99.4 by 1000 shifts the decimal three places to the right, transforming it into 99400.0.
This method simplifies the process by treating decimals as whole numbers first, and then correctly placing the decimal. Practice with different decimal places to get comfortable with this concept. Always ensure you count the decimal places correctly to avoid mistakes.
A key point to remember is that multiplying by 10, 100, 1000, etc. shifts the decimal point to the right.
For example, in our exercise problem, multiplying 99.4 by 1000 shifts the decimal three places to the right, transforming it into 99400.0.
This method simplifies the process by treating decimals as whole numbers first, and then correctly placing the decimal. Practice with different decimal places to get comfortable with this concept. Always ensure you count the decimal places correctly to avoid mistakes.
Basic Arithmetic
Basic arithmetic involves the foundational operations (addition, subtraction, multiplication, and division) that are essential for solving math problems.
In our example, the focus is on multiplication, one of the four basic arithmetic operations.
Breaking down the problem step-by-step can make it easier to solve. Begin by identifying the numbers you need to multiply.
Next, multiply them as if they were whole numbers. Finally, adjust for any decimals by placing the decimal point in the appropriate position in your answer.
This systematic approach helps in managing more complex numbers and ensures accuracy in problem-solving.
In our example, the focus is on multiplication, one of the four basic arithmetic operations.
Breaking down the problem step-by-step can make it easier to solve. Begin by identifying the numbers you need to multiply.
Next, multiply them as if they were whole numbers. Finally, adjust for any decimals by placing the decimal point in the appropriate position in your answer.
This systematic approach helps in managing more complex numbers and ensures accuracy in problem-solving.
Step-by-Step Math Solutions
Step-by-step solutions are incredibly helpful in understanding math problems. Let's break down the provided example to illustrate this approach.
First, understand the problem: you need to multiply 99.4 by 1000.
Next, set up the problem clearly: align the numbers properly as shown \( 99.4 \times 1000 \).
Then, perform the multiplication by initially ignoring the decimal, treating the numbers as whole numbers (994 x 1000 = 994000).
Finally, adjust the decimal placement: since 99.4 has one decimal place, shift the decimal in the product one place to the right to get 99400.0.
This method ensures you do not miss any steps, thereby reducing errors and making complex problems more manageable.
First, understand the problem: you need to multiply 99.4 by 1000.
Next, set up the problem clearly: align the numbers properly as shown \( 99.4 \times 1000 \).
Then, perform the multiplication by initially ignoring the decimal, treating the numbers as whole numbers (994 x 1000 = 994000).
Finally, adjust the decimal placement: since 99.4 has one decimal place, shift the decimal in the product one place to the right to get 99400.0.
This method ensures you do not miss any steps, thereby reducing errors and making complex problems more manageable.
- Identify the numbers involved.Treat them as whole numbers.Adjust for decimal places after multiplication.
Other exercises in this chapter
Problem 266
In the following exercises, multiply. $$ (0.037)(100) $$
View solution Problem 267
In the following exercises, multiply. $$ (55.2)(1000) $$
View solution Problem 269
In the following exercises, divide. Round money monetary answers to the nearest cent. $$ \$ 117.25 \div 48 $$
View solution Problem 270
In the following exercises, divide. Round money monetary answers to the nearest cent. $$ \$ 109.24 \div 36 $$
View solution