![]() Move the decimal left until it is to the right of the first nonzero digit, which is 2. If you moved the decimal right as in a very small number, n n is negative.įor example, consider the number 2,780,418. If you moved the decimal left as in a very large number, n n is positive. Multiply the decimal number by 10 raised to a power of n. Count the number of places n that you moved the decimal point. Write the digits as a decimal number between 1 and 10. ![]() To write a number in scientific notation, move the decimal point to the right of the first digit in the number. ![]() How can we effectively work read, compare, and calculate with numbers such as these?Ī shorthand method of writing very small and very large numbers is called scientific notation, in which we express numbers in terms of exponents of 10. Other extreme numbers include the width of a human hair, which is about 0.00005 m, and the radius of an electron, which is about 0.00000000000047 m. Recall at the beginning of the section that we found the number 1.3 × 10 13 1.3 × 10 13 when describing bits of information in digital images. Simplify each expression and write the answer with positive exponents only. = 27 w 10 − ( −4 ) 4 The quotient rule and reduce fraction = 27 w 14 4 Simplify. = 1 The zero exponent rule ( x 2 2 ) 4 ( x 2 2 ) −4 = ( x 2 2 ) 4 − 4 The product rule = ( x 2 2 ) 0 Simplify. ( −2 a 3 b − 1 ) ( 5 a −2 b 2 ) = −2 ⋅ 5 ⋅ a 3 ⋅ a −2 ⋅ b −1 ⋅ b 2 Commutative and associative laws of multiplication = −10 ⋅ a 3 − 2 ⋅ b −1 + 2 The product rule = −10 a b Simplify. = v 4 u 2 The negative exponent rule ( u −1 v v −1 ) 2 = ( u −1 v ) 2 ( v −1 ) 2 The power of a quotient rule = u −2 v 2 v −2 The power of a product rule = u −2 v 2 − ( −2 ) The quotient rule = u −2 v 4 Simplify. ( u −1 v v −1 ) 2 = ( u −1 v ) 2 ( v −1 ) 2 The power of a quotient rule = u −2 v 2 v −2 The power of a product rule = u −2 v 2 − ( −2 ) The quotient rule = u −2 v 4 Simplify. = 1 17 2 or 1 289 The negative exponent rule Expand each expression, and then rewrite the resulting expression. Both terms have the same base, x, but they are raised to different exponents. Using the Product Rule of ExponentsĬonsider the product x 3 ⋅ x 4. In this section, we review rules of exponents first and then apply them to calculations involving very large or small numbers. What does this mean? The “E13” portion of the result represents the exponent 13 of ten, so there are a maximum of approximately 1.3 × 10 13 1.3 × 10 13 bits of data in that one-hour film. The maximum possible number of bits of information used to film a one-hour (3,600-second) digital film is then an extremely large number. It can also perceive a color depth (gradations in colors) of up to 48 bits per pixel, and can shoot the equivalent of 24 frames per second. A particular camera might record an image that is 2,048 pixels by 1,536 pixels, which is a very high resolution picture. For instance, a pixel is the smallest unit of light that can be perceived and recorded by a digital camera. But it may not be obvious how common such figures are in everyday life. ![]() Mathematicians, scientists, and economists commonly encounter very large and very small numbers. Find the power of a product and a quotient.Use the zero exponent rule of exponents.
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