Scientific Notation

Describe what to do when ADDING scientific notation

-EXPONENTS NEED TO BE THE SAME! If they are the same already ((1.2 X 10 to the 2nd) + (1.4 X 10 to the 2nd) = 2.6 X 10 to the 2nd) just add the decimals and keep the exponent the same -IF EXPONENTS ARE NOT THE SAME, MAKE THEM THE SAME ((3.5 X 10 to the 5th) + (2 X 10 to the 6th)) ----> move the decimal point one place to the LEFT and ADD ONE to the exponent to make it the same ----> ((.35 X 10 to the 6th) + (2 X 10 to the 6th)) -LA RS = LEFT/ADD and RIGHT/SUBTRACT

Describe what to do when SUBTRACTING in scientific notation

-EXPONENTS NEED TO BE THE SAME! If they are the same already ((7.6 X 10 to the 5th) - (1.6 X 10 to the 5th) = 6 X 10 to the 5th -IF EXPONENTS ARE NOT THE SAME, MAKE THEM THE SAME ((9.8 X 10 to the 4th) - (3.3 X 10 to the 5th) ---> Move the 3.3 decimal one place to the RIGHT and SUBTRACT THE EXPONENT ---> 9.47 X 10 to the 4th power -LA RS = LEFT/ADD and RIGHT/SUBTRACT

Describe what to do when DIVIDING scientific notation

Divide the whole numbers/decimals together and then subtract your exponents in the power of 10. Example: (4 X 10 to the 7th power) / (2.5 X 10 to the 2nd power) = 1.6 X 10 to the 5th power

What does a negative exponent in scientific notation mean? Write the below example in standard form. Example: 4.5 X 10 to the -5th power

It means that you move the decimal point to the left to get to standard form. In this example, you would move the decimal point 5 places to the left to get 0.000045

What does a positive exponent in scientific notation mean? Write the below example in standard form. Example: 5.65 X 10 to the 4th power

It means that you move the decimal point to the right to get to standard form. In this example, you would move 4 places to the right to get 56,500

Describe what to do when MULTIPLYING scientific notation

Multiply the whole numbers/decimals together and then add your exponents in the power of 10. Example: (1.5 X 10 to the 3rd power) X (5 X 10 to the 2nd power) = 7.5 X 10 to the 5th power

What do you do if you end up with an answer that says 890 X 10 to the 2nd power? Is this scientific notation?

No this is not scientific notation, the first number needs to be between 1 and 10. You need to move the decimal 2 places to the left. LA RS says when you move to the left, you add to the exponent. You would end up with 8.9 X 10 to the 4th power.

What do you do if you end up with an answer that says 0.073 X 10 to the 6th power? Is this scientific notation?

No this is not scientific notation. You would need to move the decimal point 2 places to the right so the decimal is between 1 and 10. When you move 2 places to the right, LA RS says you also subtract from the decimal. Answer: 7.3 X 10 to the 4th power

Write 0.00089004 in scientific notation

You need to move the decimal point 4 places to the right so the number is between 1 and 10. Answer: 8.9004 X 10 to the -4th power

Write 99,800,000 in scientific notation

You need to move the decimal point 7 places to the left so the number is between 1 and 10. Answer: 9.98 X 10 to the 7th power