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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
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
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:
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
Equivalently, by adding zeroes, you can express the numerator and the denominator as the
same units, then simplify:
⎯ = ⎯ = 45 ten thousandths ÷ 900 ten–thousandths = ⎯...
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- Spring '07