Express following measurements in scientific notation.
1. a) 5800 m
I don't even get what scientific notation is. In my book its ays, that in Scientific notation, the numerical part of a measurement is expressed as a number between 1 and 10 multiplied by a whole-number power of 10.
So does that mean that the whole number is always going to be 10?
How exactly do I do this? I don't get how to convert:\
Where do you get the decimal from?
And where do the 2 and 3 come from? I don't understand.
its going to be 58x10^2
or 5.8x10^3
To express a measurement in scientific notation, you need to write the numerical part of the measurement as a number between 1 and 10 multiplied by a power of 10. The power of 10 represents the number of zeros in the original measurement.
For example, to express 5800 m in scientific notation:
1. Identify the numerical part of the measurement: 5800
2. Determine where to place the decimal point so that the result is a number between 1 and 10. In this case, the decimal point should be placed after the first digit, giving us 5.800.
3. Count the number of zeros between the original decimal place and the new decimal place. In this case, there are three zeros. Therefore, the power of 10 is -3 (negative because the decimal place moved to the left).
4. Write the measurement in scientific notation: 5.800 x 10^-3.
Therefore, 5800 m expressed in scientific notation is 5.800 x 10^-3.
Scientific notation is a way to express numbers that are very large or very small in a concise and standardized format. In scientific notation, the numerical part of a measurement is expressed as a number between 1 and 10, multiplied by a power of 10.
The whole number in scientific notation does not have to be 10. It can be any whole number, positive or negative, depending on the magnitude of the original number.
Now let's convert the given measurement, 5800 m, into scientific notation.
To determine the number between 1 and 10 that will be multiplied by a power of 10, we need to move the decimal point in 5800 so that there is only one non-zero digit to its left. In this case, the non-zero digit is 5.
Starting with 5800, count the number of places you need to move the decimal point to the left to get a number between 1 and 10. In this case, you need to move the decimal point three places to the left.
Now, express the number between 1 and 10 as 5.8.
Next, determine the power of 10 that corresponds to the number of places you moved the decimal point. Since the decimal point was moved three places to the left, the power of 10 will be -3.
Therefore, the scientific notation for 5800 m is 5.8 x 10^3.
Keep in mind that scientific notation is a way to represent numbers compactly and express the magnitude of a measurement. It is particularly useful when dealing with very large or very small numbers, such as those encountered in scientific and mathematical calculations.
Oh dear !!!
This is just whacky:
Therefore, 5800 m expressed in scientific notation is 5.800 x 10^-3.
5.800*10^-3 would be 0. 005800
You mean
Therefore, 5800 m expressed in scientific notation is 5.800 x 10^+3 !!!!!!!
Moreover 5.800 x 10^+3
is not the same as 5.8 x 10^-3 because that has only two significant figures. 5.8 to two figures could be could be 5.844 and not 5.800
10^x = 1 and x zeros
10^0 = 1
10^1 = 10
10^2 = 100
10^3 = 1000 etc
10^-1 = 1/10 =0.1
10^-2 = 1/100 = 0.01
10^-3 = 1/1000 = 0.001 etc