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How many 40s are in 800? Too hard a question? Then lop the last 0 off of both of them and ask yourself how many 4s there are in 80. It’s really the same question in a slightly different form. Did you get a quotient of 20 and a little more? That’s close enough for an estimate. Keep it in the back of your mind, or pencil it into the margin while we work the problem. This is not something you’d want to try solving by short division, but you don’t have to get too formal either. Look at the dividend and the divisor: 854 divided by 37.

Look at the dividend and the divisor: 854 divided by 37. Well, you know there are at least ten 37s in there, so let’s write them under the 854 and subtract. 37 854 370 10 484 The 10 out on the side keeps track of how many 37s you’re subtracting. 854 – 370 = 484. You could call 484 the remaining dividend, and 10 the partial quotient. Next, since I know there are another ten 37s in 484, I’ll subtract another ten 37s: 37 854 370 10 484 370 10 114 We have a new partial quotient out on the step of “the ladder,” and the remaining dividend is 114.

1. 2. 3. 4. 33 ⁄ 8 × 42 ⁄ 3 = ? 55 ⁄ 6 × 67 ⁄ 12 = ? 74 ⁄ 9 ÷ 23 ⁄ 4 = ? 95 ⁄ 8 ÷ 315 ⁄ 16 = ? Answers 1. 2. 3. 4. qxd 4/2/07 11:58 PM Page 56 5 Decimal Fractions You use decimal fractions every day, since our system of dollars and cents is based on them. “Deci-” is a prefix meaning tenth, and so decimal fractions extend the place value system of numeration to the right, where a decimal point separates the whole numbers from the fractions. The whole numbers are to the left of the decimal point and the fractions to the right.

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A course on Modular localization and algebraic approach to nonperturbative QFT by Schroer B.


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