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Suppose p = a*10^x and
q = b*10^y are two numbers in scientific notation.
Then p*q = (a*b)*10^(x+y)
where, 1 <= |a|,|b| < 10 implies that 1 <= |a*b| < 100.
If a*b is greater than or equal to 10, let a*b = 10*c
then in scientific notation, p*q = c*10^(x+y+1).
Also p/q = (a/b)*10^(x-y)
where, 1 <= |a|,|b| < 10 implies that 0 < |a/b| <= 1.
If a/b is less than 1, let a/b = c/10
then in scientific notation, p/q = c*10^(x-y-1).
Scientific notation is a way of representing numbers, usually very large or very small, in the form a*10^b where 1 ≤ |a| < 10 is a decimal number and b is an integer (negative or positive). a is called the mantissa and b is called the exponent. To convert a number to scientific notation: · If the number has no decimal point, then add one at the end. · Then move the decimal point to just after the first digit while counting the number of places you have moved it. · The mantissa of the new number, formed after moving the decimal point is a. · If the original number is negative, then so is a. · The number of places to the left that the decimal point was moved is b. If it was moved to the right, then b is negative.
Suppose p = a*10^x and q = b*10^y are two numbers in scientific notation. Then p*q = (a*b)*10^(x+y) where, 1 <= |a|,|b| < 10 implies that 1 <= |a*b| < 100. If a*b is greater than or equal to 10, let a*b = 10*c then in scientific notation, p*q = c*10^(x+y+1). Also p/q = (a/b)*10^(x-y) where, 1 <= |a|,|b| < 10 implies that 0 < |a/b| <= 1. If a/b is less than 1, let a/b = c/10 then in scientific notation, p/q = c*10^(x-y-1).
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How is a number expressed in scientific notation?
Scientific notation is when you multiply a number that is between 1 and 10 to 10 to a power. for example: I want to write 3,946,000,000 as a scientific notation. What I do is I divide the number by 10 over and over until the number is 3.946 then how many times I divided 3,946,000,000 by 10 is the exponent of 10 which you multiply by 3.946 and the Scientific notation of 3,946,000,000 is 3.946 * 109.
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.
Why was scientific notation invented?
the scientific notation was created to make it easier to multiply by ten EX: 3*104=? 3 with 4 zeros 30000
How do you do scientific notation in Algebra 1?
same as in any other class, n x 10k , where n is between 1 and 10, and k is an integer exponent to describe how many times to multiply or divide by 10 to restore to normal notation.
How do you make 300 cakes instead of one by using scientific notation with three significant figures?
You multiply each ingredient by 300. There is no need for scientific notation.
How is a number expressed in scientific notation?
Scientific notation is when you multiply a number that is between 1 and 10 to 10 to a power. for example: I want to write 3,946,000,000 as a scientific notation. What I do is I divide the number by 10 over and over until the number is 3.946 then how many times I divided 3,946,000,000 by 10 is the exponent of 10 which you multiply by 3.946 and the Scientific notation of 3,946,000,000 is 3.946 * 109.
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.
Multiply or divide as indicated and express in correct scientific notation 2.85e7 x 3.16e-3?
It is 9.006*10^4.
How do you divide and multiply notations?
You do not divide or multiply notations: you perform those operations on numbers which are expressed in different notations. How you do that depends on which notation you are concerned with.
Why is it important to have a method of denoting numbers that are very small or very large with a minimal amount of writing?
Scientific notation makes it easy to write down numbes, and to compare them (if normalized scientific notation is used). It is also fairly easy to multiply and divide them, once you know what you are doing.
Why was scientific notation invented?
the scientific notation was created to make it easier to multiply by ten EX: 3*104=? 3 with 4 zeros 30000
How do you do scientific notation in Algebra 1?
same as in any other class, n x 10k , where n is between 1 and 10, and k is an integer exponent to describe how many times to multiply or divide by 10 to restore to normal notation.
How do you make 300 cakes instead of one by using scientific notation with three significant figures?
You multiply each ingredient by 300. There is no need for scientific notation.
0.000714 in scientific notation?
We multiply or divide the number by powers of 10 so that the first digit in the number is between 1 and 10. So 0.000714 = 7.14 x 10-4
What are rules of adding subtracting dividing multiplying 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 Notation Multiplication 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 is 1000000 multiply by 100000?
100000000000
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.
