Decimal numbers have reciprocals too! To find the reciprocal of a decimal number, change it to a fraction, then flip the fraction. Not sure how to convert a decimal number to a fraction? Check out our lesson on converting percentages, decimals, and fractions. If you've ever multiplied and divided fractions , the reciprocal might seem familiar to you.
If not, you can always check out our lesson on multiplying and dividing fractions. When you multiply two fractions, you multiply straight across. The numerators get multiplied, and the denominators get multiplied. However, when you divide by a fraction you flip the fraction over so the numerator is on the bottom and the denominator is on top.
In other words, you use the reciprocal. You use the opposite number because multiplication and division are also opposites. Use the skills you just learned to solve these problems. After you've solved both sets of problems, you can scroll down to view the answers. Observe the table to see how the number is written in its reciprocal form and how the sign of the powers changes.
We have a set of rules or laws for negative exponents which make the process of simplification easy. Given below are the basic rules for solving negative exponents. A negative exponent takes us to the inverse of the number. This is how negative exponents change the numbers to fractions. Let us take another example to see how negative exponents change to fractions. Therefore, negative exponents get changed to fractions when the sign of their exponent changes. Multiplication of negative exponents is the same as the multiplication of any other number.
As we have already discussed that negative exponents can be expressed as fractions, so they can easily be solved after they are converted to fractions. After this conversion, we multiply negative exponents using the same rules that we apply for multiplying positive exponents. Let's understand the multiplication of negative exponents with the following example.
Solving any equation or expression is all about operating on those equations or expressions. Similarly, solving negative exponents is about the simplification of terms with negative exponents and then applying the given arithmetic operations. When we have negative numbers as exponents, we call them negative exponents. For example, in the number 2 -8 , -8 is the negative exponent of base 2. This is not true that negative exponents give negative numbers.
Being positive or negative depends on the base of the number. Negative numbers give a negative result when their exponent is odd and they give a positive result when the exponent is even.
A perfect square number can be represented as a square shape, as shown below. We see that 1, 4, 9, 16, 25, and 36 are examples of perfect squares. To square a number, multiply the number by itself. Below are some more examples of perfect squares. The inverse operation of squaring a number is called finding the square root of a number.
Square roots are written with the mathematical symbol, called a radical sign , that looks like this:. Think, what number times itself gives 81? The square root of 36 is the number that you can multiply by itself to get The square root is not the number you multiply by 2 to get You may have incorrectly added 36 to itself to get Exponential notation is a shorthand way of writing repeated multiplication of the same number.
A number written in exponential notation has a base and an exponent, and each of these parts provides information for finding the value of the expression. The base tells what number is being repeatedly multiplied, and the exponent tells how many times the base is used in the multiplication.
Exponents 2 and 3 have special names. The inverse of squaring a number is finding the square root of a number. Example Problem Find the value of 4 2. Example Problem Find the value of 2 5. The base is 2, the number being multiplied. B 64 Correct. C Incorrect. D 43 Incorrect. B 60 Incorrect. C 10 5 Incorrect. D 10 6 Correct. Example Problem Find. B 18 Incorrect.
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