Explain how to add, subtract, multiply, and divide in scientific notation.
Adding and subtracting in scientific notation:
To add or subtract numbers written in scientific notation, you need to make sure the exponents are the same. Once you have the same exponents, you can simply add or subtract the coefficients.
1. Start by identifying the two numbers you want to add or subtract in scientific notation. For example, let's say we have 2.5 x 10^4 and 3.8 x 10^3.
2. Adjust the exponents so they are the same. In this case, we can rewrite 3.8 x 10^3 as 0.38 x 10^4. Now both numbers have 10^4 as the exponent.
3. Once you have the same exponents, you can add or subtract the coefficients. In our example, we would add 2.5 + 0.38 = 2.88.
4. The final step is to rewrite the sum or difference in scientific notation by keeping the same exponent. In our example, the answer would be 2.88 x 10^4.
Multiplying in scientific notation:
To multiply numbers written in scientific notation, you need to multiply the coefficients and add the exponents.
1. Take the two numbers you want to multiply in scientific notation. Let's say we have 2.7 x 10^3 and 1.5 x 10^2.
2. Multiply the coefficients: 2.7 * 1.5 = 4.05.
3. Add the exponents: 10^3 * 10^2 = 10^(3+2) = 10^5.
4. Rewrite the answer in scientific notation by keeping the same coefficient and the new exponent. In our example, the product would be 4.05 x 10^5.
Dividing in scientific notation:
To divide numbers written in scientific notation, you need to divide the coefficients and subtract the exponents.
1. Take the two numbers you want to divide in scientific notation. For example, let's consider 8.1 x 10^7 divided by 3 x 10^2.
2. Divide the coefficients: 8.1 / 3 ≈ 2.7.
3. Subtract the exponents: 10^7 / 10^2 = 10^(7-2) = 10^5.
4. Rewrite the answer in scientific notation by keeping the same coefficient and the new exponent. In our example, the quotient would be 2.7 x 10^5.