One of your friends missed the class on scientific notation. Describe how you would explain to your friend what it means for a number to be in scientific notation and how to convert a number from standard form to scientific notation.
(please write how you would explain it {the formula and stuff} i promise i will not use word for word i will put it in my own words but please help me! i have a hard time in math!!)
A number in scientific notation consists of two parts:
Some number where the decimal is after the first digit and that is times a power of 10
e.g.
3.456 * 10^3
which in normal notation is 3.456 * 1000 = 3456
to change a given number to scientific notation, look at where the
decimal is currently. If it is a whole number, the decimal will be at the end
of the number. You want the decimal to be after the first digit, so count the
number of spaces it must be moved. That number of spaces will become
your exponent for the power of 10.
If you had to move the decimal to the left, that means that your number was "large" and the exponent will be positive
e.g. 3456.86 = 3.45686 * 10^3
If you had to move the decimal to the right, that means that your number
was "small" and the exponent will be negative.
e.g. 0.00003456 = 3.456 * 10^-5
generally you cannot add or subtract them if the powers of 10 are different without changing them to regular numbers
to multiply or divide them, perform the operations on each part, you may have to simplify your answer.
e.g.
(3.45 * 10^2 )(22.31 * 10^-5)
= (3.45*22.31) * (10^2 * 10^-5)
= 76.9695 * 10^-3
= 7.69695 * 10^-2 , (easy way to look at what I did: I made the first part smaller, so I had to make the power of 10 bigger)
That's about it
PLEASE SOMEONE I REALLY NEED THIS ANSWER!!!! MY ANSWER HAS TO BE TURNED IN SOON PLEASE HELP ME! :(
Thank you so much mathhelper this has helped me so much thank you!!!
Sure! I can help you explain scientific notation and how to convert a number from standard form to scientific notation.
Scientific notation is a way of writing very large or very small numbers in a concise and standardized format. It is commonly used in scientific and mathematical calculations. The notation consists of two parts: a coefficient and an exponent.
To convert a number from standard form to scientific notation, follow these steps:
Step 1: Identify the coefficient.
The coefficient is the non-zero digit in the number that comes before the decimal point in standard form. For example, in the number 3,245.67, the coefficient is 3.
Step 2: Determine the exponent.
The exponent represents the number of places the decimal point needs to be moved to reach the desired coefficient. If the original number is greater than or equal to 1, the exponent will be positive, and if the original number is smaller than 1, the exponent will be negative.
Move the decimal point to the right until it is immediately after the last non-zero digit in the coefficient. Count the number of places you moved the decimal point. If you moved to the right, the exponent will be positive. If you moved to the left, the exponent will be negative. For example, in the number 3,245.67, the decimal point needs to be moved four places to the left to reach 3,24567. This means the exponent is -4.
Step 3: Write the scientific notation.
Write the coefficient, followed by the letter "x" (multiplication symbol), and then write 10 raised to the power of the exponent. For the example of 3,245.67, the scientific notation would be written as 3.24567 x 10^-4.
When explaining it to your friend, you can use these steps and emphasize that scientific notation helps in representing extremely large or small numbers in a convenient and standardized way. Encourage them to practice the conversion with different numbers to gain familiarity.
Remember, practice is key in mastering mathematical concepts. If your friend has any further questions or needs additional help, feel free to ask!