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In converting numbers into scientific notation, first you should move the decimal point such that there would be one significant figure to the left of the decimal point.

Examples:

299792458 -> 2.99792458

0.0000000000667428 -> 6.67428

Then, count the number of times you moved the decimal point. Note the direction of movement.

Examples:

299792458 -> 2.99792458 (8 digits to the left)

0.0000000000667428 -> 6.67428 (11 digits to the right)

Lastly, express the number as a product of the modulus (the number with the decimal point moved) and a power of ten.

Examples:

299792458 -> 2.99792458 x 108 (If the decimal point was moved to the left, the power is positive)

0.0000000000667428 -> 6.67428 x 10-11 (If the decimal point was moved to the right, the power is negative)

Q: Rules of converting numbers to scientific notation?

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In scientific notation all numbers are written in the form: a*10b where a is a decimal number such that 1 â‰¤ a < 10 and b is an integer.

Scientific notation is of little use for long mathematical expressions. It is used to express very large or very small numbers - not expressions.

20,000 + 3,400,000

Standard notation (in the UK) is the same as scientific notation. So the one rule to use is DO NOTHING!

I don't know what you mean "how to write the rules." In the US, "standard" notation means "long form", i.e. 6,000,000, while "scientific" notation means the exponential form, 6x106. I had thought it was the same in the UK, but Mehtamatics says otherwise: "Standard notation and scientific notation are the same in terms of UK usage of these phrases."

Related questions

When adding or subtracting numbers in scientific notation, ensure that the exponents are the same. If the exponents are not the same, adjust one or both numbers to match. Then, add or subtract the coefficients while keeping the exponent the same. Finally, simplify the result if necessary by converting it back to proper scientific notation.

In scientific notation all numbers are written in the form: a*10b where a is a decimal number such that 1 â‰¤ a < 10 and b is an integer.

to convert scientific notation to decimal you count the number of spaces up to the last digit then put the decimal point then put x10 to the power of if how many places you move the decimal point.................................

Scientific notation is of little use for long mathematical expressions. It is used to express very large or very small numbers - not expressions.

20,000 + 3,400,000

Standard notation (in the UK) is the same as scientific notation. So the one rule to use is DO NOTHING!

I don't know what you mean "how to write the rules." In the US, "standard" notation means "long form", i.e. 6,000,000, while "scientific" notation means the exponential form, 6x106. I had thought it was the same in the UK, but Mehtamatics says otherwise: "Standard notation and scientific notation are the same in terms of UK usage of these phrases."

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Scientific notation is a useful way of dealing with very large and very small numbers. It allows them to be presented in a form where their magnitude can be seen more easily. Also it can simplify calculations by allowing you to concentrate on the significant digits rather than the orders of magnitude which are very easily dealt with. This latter advantage has somewhat diminished with the widespread availability of calculators and computers. But previously people used log tables and slide rules for multiplication and division. These calculating devices depended on thinking of numbers in their scientific notation.

1 With addition change the scientific notation back to 'normal numbers' and then add accordingly 2 With subtraction change the scientific back to 'normal numbers' and then subtract accordingly 3 With division subtract the exponents and divide the decimals 4 With multiplication add the exponents and multiply the decimals 5 Note that if changes occur below 1 or greater than 9 in the decimal element of the scientific notation then appropriate adjustments must be made

If it is unambiguous and can be recognized by a computer it's probably OK. For very large or very small numbers the format is normally n.nnnnn x 10m in the form n.nnnnnEm or similar. All integers have to be written out exactly.

To subtract numbers in scientific notation, first convert both numbers to the same exponent by moving the decimal point. Then, subtract the mantissas (the first part of the number) and keep the common exponent. Finally, normalize the result by adjusting the decimal point and exponent if needed.