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The answer has a zero to the right of the decimal to keep two significant digits Place two zeros to the right of the calculator answer to keep four significant digits

The next: method also calls another internal method, transitionOutToLeft, which will take the current view and shuffle it off to the left. Its implementation looks like this:

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A cube root of a number is one of its three equal factors A radical sign with the 3 1 number 3, , indicates a cube root A cube root also can be shown as exponent , as in

3 3 3

b 3

Example: Simplify the following cube root terms 125 39304 (500)(500)(500) 34000 500

- (void)transitionOutToLeft { NSRect newFrame = [middleView frame]; newFrame.origin.x -= newFrame.size.width; [[middleView animator] setFrame:newFrame]; [[middleView animator] setAlphaValue:0.0]; }

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In the following operations with exponents, a and b can be numbers or variables Product of powers To multiply terms with the same base, add the exponents, as in (a m ) (a n ) a m n Quotient of powers To divide terms with the same base, subtract the bottom exponent from the top exponent, as in a m/a n a m n Power of a power To calculate the power of a power, use the same base and multiply the exponents, as in (a m ) n a mn n th root of a power To calculate the root of a power, use the same base and m n am a n divide the power exponent by the root exponent, as in

c (d 2n)2

The absolute value of a number, n, is its magnitude, regardless of its sign The absolute value of n is written as n Because magnitudes cannot be less than zero, absolute values always are greater than or equal to zero Examples: 3 3 3 3

A number of the form a 10n is written in scientific notation, where 1 a 10, and n is an integer The base, 10, is raised to a power, n The term a must be less than 10

Connecting Math to Physics Physicists use scientific notation to express, compare, and calculate with measurements that are greater than 10 or less than 1 For example, the mass of a proton is written as 673 10 28 kg The density of water is written as 1000 103 kg/m3 This shows, using significant digit rules, that this measurement is exactly 1000 to four significant digits However, writing the density of water as 1000 kg/m3 would imply that it has only one significant digit, which is incorrect Scientific notation helps physicists keep accurate track of significant digits

With that in place, you re now ready to Build & Run once again. This time you ll see that not only does the initial view setup work, but now you can also hit the Next button to transition to the next view! Smooth. See Figure 14 9.

Multiplying by a power of 10 is like moving the decimal point that same number of places to the left (if the power is negative) or right (if the power is positive) To express a large number in scientific notation, first determine the value for a, 1 a 10 Count the number of decimal places from the decimal point in a to the decimal point in the number Use that count as the power of 10 A calculator shows scientific notation with e for exponent, as in 24e 11 24 1011 Some calculators use an E to show the exponent, or there is often a place on the display where the calculator can show smaller-sized digits representing the exponent Example: Write 7,530,000 in scientific notation The value for a is 753 ( The decimal point is to the right of the first nonzero digit) So the form will be 753 10n 7,530,000 753 106

To write the standard form of a number expressed in scientific notation, write the value of a, and place extra zeros to the right of the number Use the power and move the decimal point in a that many places to the right Example: Write the following number in standard form 2389 105 238900 105 238,900

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