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To express a small number in scientific notation, first determine the value for a, 1 a 10 Then count the number of decimal places from the decimal point in a to the decimal point in the number Use that number as the power of 10 Multiplying by a number with a negative power is the same as dividing by that number with the corresponding positive power Example: Write 0000000285 in scientific notation The value for a is 285 (The decimal point is to the right of the first nonzero digit) So the form will be 285 10n 0000000285 285 10

Remember that the table constraints defined when creating the table apply, so you must enter data for columns created with the NOT NULL constraint If a column was created with a DEFAULT VALUE constraint, you can use the keyword DEFAULT in the valuelist to assign the default value to the column data You can also skip columns that have default values by not listing them in the columnlist parameter Those columns will automatically be assigned their default values

To express a small number in standard form, write the value for a and place extra zeros to the left of a Use the power and move the decimal point in a that many places to the left Example: 16 10

000016 10

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Now all that s left is to implement matching methods for rightward transitions. These methods are all pretty similar to the others, and are presented here without further comment, except one: you may be tempted to copy and paste the existing methods and make whatever you changes you can spot, but be careful! Some of the differences are subtle but important.

Calculating with numbers written in scientific notation uses the properties of exponents (see page 840) Multiplication Multiply the terms and add the powers of 10 Example: Simplify (40 10 8)(12 105) (40 12)(10 (48)(10 8 5) (48)(10 3) 48 10 3

105)

96 0 107 160 103 60 ( 960 ) ( 10 ) 1 10

600 107 600 104

Addition and subtraction Adding and subtracting numbers in scientific notation is more challenging, because the powers of 10 must be the same in order to add or subtract the numbers This means that one of the numbers may need to be rewritten with a different power of 10 If the powers of 10 are equal, then use the distributive property Example: Simplify (32 105 ) (48 105 ) (32 48) 105 80 105 (32 105 ) (048 105 ) (32 048) 105 368 105 37 105

Example: Simplify (32 105 ) (48 104 )

- (void)prepareLeftSide { NSInteger previousTabIndex = currentTabIndex-1; if (previousTabIndex < 0) previousTabIndex = [items count]-1; leftView = [[items objectAtIndex:previousTabIndex] view];

Rewrite 48 104 as 048 105 Group terms Add terms Round using addition/subtraction rule for significant digits

13 Evaluate each expression Express the result in scientific notation a (52 10

4 )(40

108 )

b (24 103 )

NSRect viewFrame = [box bounds]; viewFrame.origin.x -= viewFrame.size.width; [leftView setFrame:viewFrame]; [leftView setAlphaValue:0.0]; [box addSubview:leftView]; } - (void)transitionInFromLeft { [[leftView animator] setFrame:[box bounds]]; [[leftView animator] setAlphaValue:1.0]; } - (void)transitionOutToRight { NSRect newFrame = [middleView frame]; newFrame.origin.x += [box bounds].size.width; [[middleView animator] setFrame:newFrame]; [[middleView animator] setAlphaValue:0.0]; } - (IBAction)previous:(id)sender { [self prepareLeftSide]; [NSAnimationContext beginGrouping]; [[NSAnimationContext currentContext] setDuration:ANIM_DURATION]; [self transitionInFromLeft]; [self transitionOutToRight]; [NSAnimationContext endGrouping]; currentTabIndex--; if (currentTabIndex < 0) currentTabIndex = [items count]-1; rightView = middleView; middleView = leftView; }

(80 104 )

Scientists and mathematicians have agreed on a set of steps or rules, called the order of operations, so that everyone interprets mathematical symbols in the same way Follow these steps in order when you evaluate an expression or use a formula 1 Simplify the expressions inside grouping symbols, like parentheses ( ), brackets [ ], braces { }, and fraction bars 2 Evaluate all powers and roots 3 Do all multiplications and/or divisions from left to right 4 Do all additions and/or subtractions from left to right Example: Simplify the following expression 4 3(4 1) 23 4 3(3) 23 4 3(3) 8 4 9 8 8

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