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Unformatted text preview: The first number gets smaller by a factor of 10 as we move the decimal one place to the left,
but the second number gets bigger by a factor of 10 to compensate. Manhattan GMAT Prep
* 16 the new standard DIGITS & DECIMALS STRATEGY Chapter 1 The Last Digit Shortcut
Sometimes the GMAT asks you to find a units digit, or a remainder after division by 10.
What is the units digit of (7)2(9)2(3)3?
In this problem, you can use the Last Digit Shortcut:
To find the units digit of a product or a sum of integers, only pay attention to the
units digits of the numbers you are working with. Drop any other digits.
This shortcut works because only units digits contribute to the units digit of the product.
STEP 1:
STEP 2:
STEP 3:
STEP 4: 7 × 7 = 49
9 × 9 = 81
3 × 3 × 3 = 27
9 × 1 × 7 = 63 Drop the tens digit and keep only the last digit: 9.
Drop the tens digit and keep only the last digit: 1.
Drop the tens digit and keep only the last digit: 7.
Multiply the last digits of each of the products. Use the Heavy Division
Shortcut when you need
an approximate answer. The units digit of the final product is 3. The Heavy Division Shortcut
Some division problems involving decimals can look rather complex. But sometimes, you
only need to find an approximate solution. In these cases, you often can save yourself time
by using the Heavy Division Shortcut: move the decimals in the same direction and round
to whole numbers.
What is 1,530,794 ÷ (31.49 × 104) to the nearest whole number?
1,530,794
31.49 × 104
1,530,794
Step 2: Rewrite the problem, eliminating powers of 10:
314,900
Step 3: Your goal is to get a single digit to the left of the decimal in the denominator. In
this problem, you need to move the decimal point backward 5 spaces. You can do this to
the denominator as long as you do the same thing to the numerator. (Technically, what
you are doing is dividing top and bottom by the same power of 10: 100,000)
15.30794
1,530,794
=
314,900
3.14900
Step 1: Set up the division problem in fraction fo...
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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.
 Spring '07
 MEJIAS

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