# Therefore d cannot be 5 6 7 8 or 9 manhattan gmat

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Unformatted text preview: which digits could not be the value of d? In order for x to be 8.1 when rounded to the nearest tenth, the right-digit-neighbor, d, must be less than 5. Therefore d cannot be 5, 6, 7, 8 or 9. * Manhattan GMAT Prep the new standard 15 Chapter 1 DIGITS &amp; DECIMALS STRATEGY Adding Zeroes to Decimals Adding zeroes to the end of a decimal or taking zeroes away from the end of a decimal does not change the value of the decimal. For example: 3.6 = 3.60 = 3.6000 Be careful, however, not to add or remove any zeroes from within a number. Doing so will change the value of the number: 7.01 ≠ 7.1 Powers of 10: Shifting the Decimal When you shift the decimal to the right, the number gets bigger. When you shift the decimal to the left, the number gets smaller. Place values continually decrease from left to right by powers of 10. Understanding this can help you understand the following shortcuts for multiplication and division. When you multiply any number by a positive power of ten, move the decimal forward (right) the specified number of places. This makes positive numbers larger: In words thousands hundreds tens ones tenths hundredths thousandths In numbers 1000 100 10 1 0.1 0.01 0.001 In powers of ten 103 102 101 100 10−1 10−2 10−3 3.9742 × 10 3 = 3,974.2 89.507 × 10 = 895.07 (Move the decimal forward 3 spaces.) (Move the decimal forward 1 space.) When you divide any number by a positive power of ten, move the decimal backward (left) the specified number of places. This makes positive numbers smaller: 4,169.2 ÷ 102 = 41.692 89.507 ÷ 10 = 8.9507 (Move the decimal backward 2 spaces.) (Move the decimal backward 1 space.) Note that if you need to add zeroes in order to shift a decimal, you should do so: 2.57 × 106 = 2,570,000 14.29 ÷ 105 = 0.0001429 (Add 4 zeroes at the end.) (Add 3 zeroes at the beginning.) Finally, note that negative powers of ten reverse the regular process: 6,782.01 × 10−3 = 6.78201 53.0447 ÷ 10−2 = 5,304.47 You can think about these processes as trading decimal places for powers of ten. For instance, all of the following numbers equal 110,700. 110.7 11.07 1.107 0.1107 0.01107 × × × × × 103 104 105 106 107...
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## This note was uploaded on 02/07/2014 for the course MIS 304 taught by Professor Mejias during the Spring '07 term at University of Arizona- Tucson.

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