Study guides

Q: Why do exponents need to be the same when using scientific notation?

Write your answer...

Submit

Related questions

In using scientific notation, you can use the number with the decimal to solve your problem and then factor in the power after the fact.

If you are adding or subtracting two numbers in scientific notation the exponents must be the same before adding the coefficients. This is similar to 'like terms' in algebraic expressions. You can't add 5x3 and 3x2 because the exponents are not the same.

Using scientific notation reduces the need to write out very large or very small numbers as the following examples show:- 1,000,000,000,000 = 1.0*1012 in scientific notation 0.0000000001 = 1.0*10-10 in scientific notation

You multiply each ingredient by 300. There is no need for scientific notation.

This is effectively the same as lining up the decimal points when adding or subtracting ordinary decimal fractions.

You do not simply calculate scientific notation for nothing. You need a number for which you calculate the scientific notation.

You don't need to do anything. It is in scientific notation.

1.48, in scientific notation is 1.48 but, if you really need to show that you have written it in scientific notation, you could write it as 1.48*100

Such numbers would not need to be written in scientific notation but if need be it is: 1.2345*10^2

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.

To add or subtract numbers in scientific notation you first need to equalise their exponents. Having done that, you carry out the addition or subtraction on the significands and append the common exponent. Then you adjust the exponent so that the significand is between 1 and 10. For example, 1.234*104 - 2.34*102 (equalise exponents) = 123.4*102 - 2.34*102 (carry out subtraction) = (123.4-2.34)*102 = 121.06*102 (adjust exponent) = 1.2106*104

830 would not normally need be written in scientific notation. However, it would be 8.3x102

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.

Since we need to shift 5 decimal places to the right to obtain the value in scientific notation, we have 5.16 x 10-5, which has 3 sig fig [already rounded to these sig figs].

There's no need for exponents because: 2*179 = 358

1 millirem does not need scientific notation the exponent part would be 0, so it is not needed

Jobs use scientific notation when people need to compute very large or very small numbers.

Sometimes. Scientific notation is used to express very small or very large numbers. If the problem does not involve any such numbers then there is no need for scientific notation.

It took me forever to learn scientific notation because of how the exponents seem backwards. When you move the decimal to the left (towards the negative numbers in a line) your exponent will be positive. When you move the decimal to the right (towards the positive numbers in line) your exponent will be negative. So since we need a number between 1-9 in order have scientific notation we have to move our decimal one place to the left. 10.4 -> 1.04 x 101

You need scientific notation too make really big numbers ,like 15,600,000,000, to an easier way. The scientific notation of 15,600,000,000 is 1.56 x 1010You also need it to make really small small numbers , like 0.0000064, easier to use in a math problem. the scientific notation of 0.0000064 is 6.4 x10-6

If need be: 3.455*102

yes

Since the decimal place is between the leading nonzero digit and the adjacent digit on the right, there is no need to shift the decimal point. Therefore, 1.07 in scientific notation is: 1.07 * 100

5.7 x 104 This is already in scietific notation. No need to align it further.

There is no single solution to all questions involving scientific notation. Different questions have different answers and so the question will need to be more specific.