Converting the Answer to Scientific Notation

Oct 13, 2025 by miodeya.com 15 views

What is the Sum of $$4.9 \times 10^2$$ and $$6.8 \times 10^3$$?

Understanding the Problem

To find the sum of $$4.9 \times 10^2$$ and $$6.8 \times 10^3$$, we need to first understand the concept of scientific notation. Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It consists of a number between 1 and 10 multiplied by a power of 10.

Breaking Down the Numbers

Let's break down the given numbers into their components:

$4.9 \times 10^2$$ can be written as 490 (since $$10^2 = 100$$).$
$6.8 \times 10^3$$ can be written as 6800 (since $$10^3 = 1000$$).$

Adding the Numbers

Now that we have broken down the numbers, we can add them together:

490 + 6800 = 7290

Converting the Answer to Scientific Notation

To convert the answer to scientific notation, we need to express it in the form $$a \times 10^b$$, where $$a$$ is a number between 1 and 10 and $$b$$ is an integer.

In this case, we can write 7290 as $$7.29 \times 10^3$$.

Conclusion

Therefore, the sum of $$4.9 \times 10^2$$ and $$6.8 \times 10^3$$ is $$7.29 \times 10^3$$.

Why is this the Correct Answer?

This is the correct answer because we have correctly broken down the numbers into their components, added them together, and then converted the answer to scientific notation.

What if the Numbers were Different?

If the numbers were different, we would need to follow the same steps:

Break down the numbers into their components.
Add the numbers together.
Convert the answer to scientific notation.

Tips and Tricks

Here are some tips and tricks to help you solve problems like this:

Make sure to break down the numbers into their components correctly.
Use the correct exponent when converting the answer to scientific notation.
Check your answer by plugging it back into the original equation.

Common Mistakes

Here are some common mistakes to avoid:

Not breaking down the numbers into their components correctly.
Using the wrong exponent when converting the answer to scientific notation.
Not checking the answer by plugging it back into the original equation.

Real-World Applications

Scientific notation is used in many real-world applications, such as:

Calculating the distance between two points on a map.
Measuring the volume of a container.
Calculating the speed of an object.

Conclusion

In conclusion, the sum of $$4.9 \times 10^2$$ and $$6.8 \times 10^3$$ is $$7.29 \times 10^3$$. We have broken down the numbers into their components, added them together, and then converted the answer to scientific notation. This is a common problem in mathematics and is used in many real-world applications.

What is Scientific Notation?

Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It consists of a number between 1 and 10 multiplied by a power of 10.

How to Write a Number in Scientific Notation

To write a number in scientific notation, we need to express it in the form $$a \times 10^b$$, where $$a$$ is a number between 1 and 10 and $$b$$ is an integer.

Examples of Scientific Notation

Here are some examples of scientific notation:

$2.5 \times 10^3$
$4.8 \times 10^2$
$6.2 \times 10^1$

Why is Scientific Notation Useful?

Scientific notation is useful because it allows us to express very large or very small numbers in a more manageable form. This makes it easier to perform calculations and understand the magnitude of the numbers.

How to Convert a Number to Scientific Notation

To convert a number to scientific notation, we need to express it in the form $$a \times 10^b$$, where $$a$$ is a number between 1 and 10 and $$b$$ is an integer.

Examples of Converting Numbers to Scientific Notation

Here are some examples of converting numbers to scientific notation:

4567 can be written as $$4.567 \times 10^3$$
0.0004567 can be written as $$4.567 \times 10^{-4}$$

Conclusion

In conclusion, scientific notation is a useful way of expressing very large or very small numbers in a more manageable form. It consists of a number between 1 and 10 multiplied by a power of 10. We have broken down the numbers into their components, added them together, and then converted the answer to scientific notation. This is a common problem in mathematics and is used in many real-world applications.