Explain how to add, subtract, multiply, and divide in scientific notation. Make it look like it was written by an 8 th grader
Hey there! So, adding, subtracting, multiplying, and dividing in scientific notation is not as hard as it seems. Let me break it down for you, 8th-grader style!
First, let's see how to **add** or **subtract** numbers in scientific notation. Here's an example:
Let's say we want to add 5.2 x 10^4 and 3.6 x 10^3.
The first thing we need to do is make sure the exponents (those small numbers after 10) are the same. In this case, we need to change 3.6 x 10^3 to 3.6 x 10^4. To do that, we move the decimal point one place to the right, and the exponent increases by 1. So, now both numbers have the same exponent of 10^4.
Now, we can add the numbers together. This is super easy! We just add the two numbers in front of 10^4, which gives us 5.2 + 3.6 = 8.8.
Finally, we keep the same exponent (10^4) and write the answer in scientific notation, which gives us 8.8 x 10^4. And that's it!
Next up, let's check out **multiplying** and **dividing** numbers in scientific notation. Here's an example for each:
Let's start with **multiplication**. We'll multiply 4.5 x 10^5 by 2.3 x 10^3.
To multiply, we simply **multiply the numbers in front of 10** (4.5 x 2.3 = 10.35). Then, we **add the exponents** (5 + 3 = 8).
So, the answer is 10.35 x 10^8. But wait! We can make it look even nicer. We can rewrite 10.35 as 1.035 by moving the decimal point one place to the left. So, the final answer is 1.035 x 10^9.
Finally, let's look at **division**. We'll divide 9.4 x 10^7 by 6.8 x 10^4.
To divide, we simply **divide the numbers in front of 10** (9.4 ÷ 6.8 ≈ 1.382). Then, we **subtract the exponents** (7 - 4 = 3).
So, the answer is 1.382 x 10^3. Again, we can make it neater. We move the decimal point one place to the left, which gives us 13.82. Now the final answer is 1.382 x 10^3, or 13.82 x 10^2.
And there you have it, 8th-grader style! You now know how to add, subtract, multiply, and divide in scientific notation. Woohoo! Keep up the great work!