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Step-by-step explanation:
Answer :
5980000000000000000000000 Kg.
Answer:
Let's look at an example. In scientific notation, Earth's mass is 5.97×1024 kg. The 5.97 part is called the coefficient; the 24 is called the exponent. Remember, an exponent simply describes how many times you are multiplying a number by itself. 2³ is 2×2×2 which is 8 and 24 is 2×2×2×2 or 16. It's especially easy when multipling 10's:
10³ is 10 × 10 × 10 = 1000, or a one with three zeros (a thousand).
106 is 10 × 10 × 10 × 10 × 10 × 10 = 1000000, a one followed by six zeros (a million).
So 1024 is a 1 followed by twenty-four zeros, 1000000000000000000000000. The mass of the Earth (in kilograms) is 5.97 times bigger than that, so that's how we write it: 5.97×1024 kg. If you wanted to write that out not-in-scientific-notation, simply write 5.97, and then move the decimal point 24 places to the right, filling in zeros to hold the places:
Small numbers are trickier; we have to use negative exponents. Recall that a negative exponent means the inverse ("1 divided by...") of the number raised to the exponent. For instance:
2-3 = 1/2³ = 1/8
10-3 = 1/10³ = 1/1000 = 0.001 (one thousandth)
10-6 = 1/106 = 1/1000000 = 0.000001 (one millionth)
The mass of a proton, in scientific notation, is 1.67×10-27kg. To write this out not-in-scientific-notation, write 1.67 and then move the decimal point to the left 27 places, filling in zeros as needed.
The coefficient and exponent are always written as decimal numbers, not as fractions. (For example, 1.4×10², rather than 7/5×10².)
In general, we prefer to keep the coefficient between 1 and 10 (either positive or negative) by adjusting the exponent. For example, we could write the mass of a proton as 16.7×10-28 kg, or 167×10-29 kg – mathematically they are all the same! But we prefer to write it as 1.67×10-27 kg. You don’t need to do this for intermediate results when you’re doing a long calculation, just for ‘final answers’.
CALCULATING WITH SCIENTIFIC NOTATION NUMBERS Here are the rules for multiplying, dividing, adding and subtracting without a calculator.
• To multiply two scientific notation numbers, multiply the coefficients and add the exponents.
EXAMPLE: (3×101)(2.5×10-2) = 7.5×10-1
• To divide two scientific notation numbers, divide the coefficients and subtract the exponents.
EXAMPLE: (9×1020)/(3×1015) = 3×105
• Addition and subtraction are harder – you can only add or subtract numbers with the same exponent. Adjust one of the numbers so it has the same exponent as the other, and only then can you add or subtract the coefficients.
EXAMPLE: Let's say you want to add two time intervals, 2×104seconds and 3x10³seconds.
Adjust the first number so it has the same exponent as the second number, then add.
(2×104)+(3×10³) = (20×10³)+(3×10³) = 23×10³ = 2.3×104
The last step we did so the coefficient would be between 1 and 10.
What is the reasoning behind these rules? Here are two short videos that explain:
multiplication & division
addition &substraction
Using Scientific Notation on your Calculator If you are using a calculator, things are a little easier, but you still need to know what you're doing. All scientific calculators (which you must have for this course) have a special button to make it easier to use scientific notation. On most of them, it is labeled EE or EXP.
It’s impossible to give directions for every calculator on the market, but I will mention one of the more popular brands, Texas Instruments. On most of the Texas Instruments graphing calculator models, the EE is above the comma key: you have to hit the 2nd function key to access it. To type in the number 2×104, the keys you would hit are
YOU DON'T TYPE IN THE TIMES KEY, NOR THE NUMBER 10! The screen will display 2E4, where the E stands for “times ten to the power of”. This saves space on the calculator display. After you hit enter, the screen will either show 20000 or 2E4, depending on the display mode you have set. To change the mode, hit the MODE key and select Sci if you want all results displayed in scientific notation, or Normal if you don’t. In Normal mode the calculator will display scientific notation only for very large and very small numbers.
To do the whole addition problem shown above, here is the sequence of keys you would hit:
On the TI–85, TI–86 and TI–89, the EE key is its own dedicated key, so you don’t need to hit the 2nd function key to input scientific notation numbers.
If you need help learning to use scientific notation on your particular calculator, please ask.
Using an "E" or "e" to stand for "times ten to the power of" is also used in computer programming languages and spreadsheets (such as Microsoft Excel).