Dealing with very large and very small numbers

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In summary, the distance from the Earth to the Sun is approximately 90 million miles, or 144 million kilometers. The distance from the Earth to the Moon is approximately 240 thousand miles, or 400 thousand kilometers. The mass of the Earth is approximately 6 septillion kilograms, or 6 trillion trillion kilograms. The mass of an electron is approximately 9 nonillionths of a kilogram, or 90 octillionths of a gram. However, the last line of the conversation is incorrect as a nonillionth should be 10^-30 and an octillionth should be 10^-27.
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Cliff Hanley
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Are the following correct (all numbers are approximations);

d from the Earth to the Sun is 90 million miles = 9 x 10^ 7 miles = 144 million km = 1.44 x 10 ^ 8 km ?

d from the Earth to the Moon is 240 thousand miles = 2.4 x 10^ 5 miles = 400 thousand km = 4 x 10 ^ 5 km?

m of the Earth = 6 x 10 ^ 24 kg = 6 septillion kg = 6 trillion trillion kg ?

m of electron = 9 x 10 ^ -31 kg = 90 nonillionths of a kg = 9 x 10 ^ -28 g = 90 octillionths of a g ?
 
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  • #2
I think your last line is wrong.
A nonillionth should be 10^-30. So 10^-31 is 1 tenth of a nonillionth.
Same thing with octillionths, 9x 10^-28 = .9 x 10^-27, or .9 octillionths, which would be 900 nonillionths.
 
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FAQ: Dealing with very large and very small numbers

What is scientific notation and why is it used?

Scientific notation is a way of writing very large or very small numbers in a compact and convenient form. It is used to make calculations and comparisons easier, as well as to express numbers that are too large or too small to be written in standard decimal form.

How do you convert a number from scientific notation to standard form?

To convert a number from scientific notation to standard form, simply move the decimal point to the right or left depending on the exponent. If the exponent is positive, move the decimal point to the right by the number of places indicated by the exponent. If the exponent is negative, move the decimal point to the left by the number of places indicated by the absolute value of the exponent.

What is the difference between significant figures and decimal places?

Significant figures are the number of digits in a number that carry meaning, while decimal places are the number of digits after the decimal point. Significant figures are used to indicate the precision of a measurement, while decimal places are used to indicate the accuracy of a calculation.

What is the best way to round a number with a large number of digits?

The best way to round a number with a large number of digits is to use significant figures. To round to a certain number of significant figures, start from the leftmost digit and count the number of significant figures. If the next digit is 5 or greater, round the last significant figure up by 1. If the next digit is less than 5, leave the last significant figure as is.

How do you compare numbers in scientific notation?

To compare numbers in scientific notation, first compare the exponents. The number with the larger exponent is the larger number. If the exponents are equal, compare the coefficients. If the coefficients are equal, the numbers are equal.

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