put this in easy words. When adding or subtracting numbers written in scientific notation, we need to ensure that the exponents are the same. We can then perform the addition or subtraction on the coefficients while keeping the same exponent. When multiplying numbers in scientific notation, we multiply the coefficients and add the exponents. When dividing numbers in scientific notation, we divide the coefficients and subtract the exponents.
The steps involved in each case are similar as we need to rearrange the numbers to ensure the exponents are the same and then perform the operation on the coefficients. However, the operations and the ways in which we manipulate the exponents differ.
Adding or subtracting numbers written in scientific notation is generally easier as we only need to adjust the exponents and perform addition or subtraction on the coefficients. Multiplying or dividing numbers written in scientific notation involves both multiplication or division of the coefficients and manipulation of the exponents, which can be more complex.
When we add or subtract numbers in scientific notation, we make sure that the exponents are the same. Then we add or subtract the coefficients while keeping the same exponent.
When we multiply numbers in scientific notation, we multiply the coefficients and add the exponents.
When we divide numbers in scientific notation, we divide the coefficients and subtract the exponents.
Doing these calculations involves similar steps. We rearrange the numbers to have the same exponents, and then perform the operation on the coefficients. However, multiplying or dividing numbers in scientific notation is more complex because we have to do both operations with the coefficients and manipulate the exponents.
In simpler terms, when we have numbers written in scientific notation (with a coefficient and an exponent), there are different rules for adding, subtracting, multiplying, and dividing them.
When adding or subtracting numbers in scientific notation, we focus on making the exponents the same. We then perform the addition or subtraction on the coefficients while keeping the same exponent.
For example, let's say we have 2.5 x 10^3 and 1.8 x 10^3. To add them, we need to make their exponents the same, which in this case is 3. Then we can simply add the coefficients, giving us 4.3 x 10^3 as the answer.
Multiplying numbers in scientific notation involves multiplying the coefficients and adding the exponents. For example, if we have 2 x 10^4 multiplied by 3 x 10^2, we multiply the coefficients (2 x 3) to get 6, and add the exponents (4 + 2) to get 6 as well. So the answer is 6 x 10^6.
When dividing numbers in scientific notation, we divide the coefficients and subtract the exponents. For example, if we have 5 x 10^6 divided by 2 x 10^3, we divide the coefficients (5 ÷ 2) to get 2.5, and subtract the exponents (6 - 3) to get 3. So the answer is 2.5 x 10^3.
In summary, adding or subtracting numbers in scientific notation is easier as we only adjust the exponents and perform addition or subtraction on the coefficients. Multiplying or dividing numbers in scientific notation involves both multiplying or dividing the coefficients and manipulating the exponents, which can be more complex.
In simple terms, when we add or subtract numbers written in scientific notation, we have to make sure the exponents are the same. Then, we can add or subtract the numbers in front, but keep the same exponent.
When we multiply numbers in scientific notation, we multiply the numbers in front (coefficients) and add the exponents.
When we divide numbers in scientific notation, we divide the numbers in front (coefficients) and subtract the exponents.
In both cases, we have to rearrange the numbers to make the exponents the same, and then combine or manipulate the coefficients accordingly. Adding and subtracting is usually easier because we only deal with the coefficients, while multiplying and dividing require both manipulation of the coefficients and changes in the exponents.