onvert the following to scientific notation:
(i) the distance to the sun, 149 500 000 000 m
(ii) the wavelength of yellow sodium light, 0.000 000 5893 m
(iii) the radius of an atom, 0.000 000 000 2 m
Here are a couple examples for you
567,000 in scientific notation is 5.67 x10^5 You always have one number in fron to the decimal place (in the ones place) multiplied 10. If you need to make the number larger the exponet on the 10 is positive. If you need to make the number smaller, the exponent on the 10 is negative. The exponent tells you how many places you have to move to the right or the left to get the original number.
149 500 000 000 = 1.495 x 10^11
Can you do the other two?
Here is an example of a smaller number
.00006 = 6 x 10^-5
I will be happy to check your answers.
To convert the given numbers to scientific notation, we need to express them in the following form: a x 10^b, where a is a number between 1 and 10 (inclusive) and b is an integer.
(i) Distance to the sun, 149,500,000,000 m:
To express this number in scientific notation, we need to move the decimal point so that we have a number between 1 and 10. Count the number of digits we moved the decimal point to the left or right (from the original number) to obtain the new number. This gives us the exponent (b).
To move the decimal point from the given number to the left until we have a number between 1 and 10, we need to move it 11 places:
149,500,000,000 m -> 1.495 x 10^11 m
Therefore, the distance to the sun is 1.495 x 10^11 meters.
(ii) Wavelength of yellow sodium light, 0.000 000 5893 m:
In this case, we need to move the decimal point to the right until we have a number between 1 and 10. Again, count the number of digits we moved the decimal point (from the original number) to obtain the new number.
To move the decimal point from the given number to the right until we have a number between 1 and 10, we need to move it 7 places:
0.000 000 5893 m -> 5.893 x 10^-7 m
Therefore, the wavelength of yellow sodium light is 5.893 x 10^-7 meters.
(iii) Radius of an atom, 0.000 000 000 2 m:
Similarly, move the decimal point to the right or left to obtain a number between 1 and 10.
To move the decimal point from the given number to the right until we have a number between 1 and 10, we need to move it 10 places:
0.000 000 000 2 m -> 2 x 10^-10 m
Therefore, the radius of an atom is 2 x 10^-10 meters.