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You divide the decimal numbers as usual. Then subtract the bottom number's exponent from the top number's exponent. This will give you the new exponent.
For example:
6.30 x 105/2.1 x 103 = 3.0 x 105-3 = 3.0 x 102
It's much easier to do this on a scientific calculator, but it is good to know the principle behind this kind of operation.
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How do you addsubtractmultiply and divide written in scientific notation?
First you have to set it to the same power of 10. Then it can easily be added or subtracted. To multiply, you just multiply the given values and add the exponent. To divide, you divide the numbers and subtract the exponent.
Can a percent be written in scientific notation?
Yes a percent can be written in scientific notation. In fact, a percentage is already almost scientific notation. % means x10-2 So 7% is 7x10-2 For double digit percentages you would need to divide the number by 10, and take away one from the power. So 25% is 2.5x10-3 For any other numbers, you can convert the percentage to a decimal by dividing it by 100. So 584.6% is 5.846. Once you have the decimal you can convert it to scientific notation the standard way.
What are the rules in adding subtracting multiplying dividing scientific notation?
Addition and Subtraction in Scientific NotationA number written in scientific notation is written as the product of a number between 1 and 10 and a number that is a power of 10 . That is, it is written as a quantity whose coefficient is between 1 and 10 and whose base is 10 .Addition and SubtractionOne of the properties of quantities with exponents is that numbers with exponents can be added and subtracted only when they have the same base and exponent. Since all numbers in scientific notation have the same base (10), we need only worry about the exponents. To be added or subtracted, two numbers in scientific notation must be manipulated so that their bases have the same exponent--this will ensure that corresponding digits in their coefficients have the same place value.Multiplying a number by another number with the same base is equivalent to multiplying their coefficients and adding their exponents. Therefore, if we want to add two quantities written in scientific notation whose exponents do not match, we can simply write one of the powers of 10 as the product of two smaller powers of 10 , one of which agrees with the other term.Alternately, if we want to preserve the exponent of the term with the larger power of 10 , we can simultaneously multiply and divide the other term by a power of 10 , applying the rule for multiplication of exponents in one case and dividing the coefficient in the other. It is this procedure that we outline below. Once the numbers have the same base and exponents, we can add or subtract their coefficients.Here are the steps to adding or subtracting numbers in scientific notation :1.Determine the number by which to increase the smaller exponent by so it is equal to the larger exponent.2.Increase the smaller exponent by this number and move the decimal point of the number with the smaller exponent to the left the same number of places. (i.e. divide by the appropriate power of 10 .)3.Add or subtract the new coefficients.4.If the answer is not in scientific notation (i.e. if the coefficient is not between 1 and 10 ) convert it to scientific notation.Multiplication and Division in Scientific NotationMultiplication and DivisionQuantities with exponents can be multiplied and divided easily if they have the same base. Since all number in scientific notation have base 10 , we can always multiply them and divide them.To multiply two numbers in scientific notation, multiply their coefficients and add their exponents. To divide two numbers in scientific notation, divide their coefficients and subtract their exponents. In either case, the answer must be converted to scientific notation.Here are the steps to multiply two numbers in scientific notation:1.Multiply the coefficients--round to the number of significant figures in the coefficient with the smallest number of significant figures.2.Add the exponents.3.Convert the result to scientific notation.Here are the steps to divide two numbers in scientific notation:1.Divide the coefficients--round to the number of significant figures in the coefficient with the smallest number of significant figures.2.Subtract the exponents.3.Convert the result to scientific notation.
What are the rules of adding subtracting dividing and multiplying written in 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
How do write 635000 in scientific notation?
To write a number in scientific notation you first need to divide the number by a power of 10 such that the answer has units as the greatest place value. In this case, you can divide by 100,000 to get 6.35. The next step is to represent this power of 10 next to the number as a multiplication. We use 100,000 which is 105. Thus, 635,000 in scientific notation is 6.35x105
