In other words you are trading decimal places in one

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Unformatted text preview: Move the decimal point LEFT four places on the 40,000 → 4 0.0003 × 40,000 = 3 × 4 = 12 The reason this technique works is that you are multiplying and then dividing by the same power of ten. In other words, you are trading decimal places in one number for decimal places in another number. This is just like trading decimal places for powers of ten, as we saw earlier. Manhattan GMAT Prep * 18 the new standard DIGITS & DECIMALS STRATEGY Chapter 1 DIVISION If there is a decimal point in the dividend (the inner number) only, you can simply bring the decimal point straight up to the answer and divide normally. Ex. 12.42 ÷ 3 = 4.14 4.14 3 12.42 12 04 3 12 However, if there is a decimal point in the divisor (the outer number), you should shift the decimal point in both the divisor and the dividend to make the divisor a whole number. Then, bring the decimal point up and divide. Ex: 12.42÷ 0.3 → 124.2 ÷ 3 = 41.4 41.4 3 124.2 12 04 3 12 Move the decimal one space to the right to make 0.3 a whole number. Then, move the decimal one space in 12.42 to make it 124.2. Remember, in order to divide decimals, you must make the OUTER number a whole number by shifting the decimal point. Division: Divide by whole numbers! You can always simplify division problems that involve decimals by shifting the decimal point in the same direction in both the divisor and the dividend, even when the division problem is expressed as a fraction: 0.0045 45 ⎯ =⎯ 0.09 900 Move the decimal 4 spaces to the right to make both the numerator and the denominator whole numbers. Note that this is essentially the same process as simplifying a fraction. You are simply multiplying the numerator and denominator of the fraction by a power of ten—in this case, 10 4, or 10,000. Keep track of how you move the decimal point! To simplify multiplication, you can move decimals in opposite directions. But to simplify division, you move decimals in the same direction. Equivalently, by adding zeroes, you can express the numerator and the denominator as the same units, then simplify: 0.0045 5 0.0045 45 ⎯ = ⎯ = 45 ten thousandths ÷ 900 ten–thousandths = ⎯...
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