GMAT Unit Conversion and Scientific Notation Guide - The GMAT Tutor

[Pages:16]GMAT Unit Conversion and Scientific Notation Guide

Matt Kirisits Website: Email: matt@ 1

Table of Contents

1. Unit Conversion ........................................................................................................................................ 3 2. Scientific Notation .................................................................................................................................. 11

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1. Unit Conversion

The key to solving unit conversion problems is to set them up properly. The general strategy is to cancel units using conversion factors. A conversion factor is the ratio that converts one unit to another, such as 1 minute = 60 seconds 1 mile = 1.6 kilometers When using these factors to do unit conversion, write them as ratios. The two conversion factors above can be written as:

Use conversion factors to set up a multiplication problem in which the unit that you are trying to cancel is on the opposite side of the ratio. For example, if you begin with kilometers in the numerator, then put kilometers in the denominator of the conversion factor. Example 1. A car travels for 46 kilometers. How far did the car travel, in miles? (Note: 1 mile = 1.6 kilometers) (A) 26.5 (B) 28.75 (C) 32.4 (D) 73.6 (E) 75.25

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Solution: 46 kilometers ?

Set up the calculation

46 kilometers ?

Cancel out kilometers

This problem begins with kilometers in the numerator; thus, put kilometers in the denominator in the conversion factor. This will make kilometers cancel out, leaving you with miles. Now simply do the calculation ? divide 46 by 1.6.

46 ? 1.6 = 28.75 miles

Answer: B

The method of setting up a multiplication problem using conversion factors can be used on all unit conversion problems. When you set up unit conversion problem in this way, it will prevent you from multiplying when you should have divided, or vice versa. On the GMAT, it is likely that the wrong answer choices will test this common mistake. In the above problem, if you multiplied 46 by 1.6, the result would be 73.6 (answer choice D).

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Unit conversion problems will often involve converting units of time, such as converting hours to seconds or vice versa. Example 2. How many seconds are in two hours? (A) 3,600 (B) 6,000 (C) 7,200 (D) 8,000 (E) 14,400

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Solution:

2 hours ?

?

Set up the calculation

2 hours ?

?

Cancel out hours, then cancel out minutes

The solution is set up to cancel out hours and minutes, leaving you with seconds. After cancelling the units, do the calculation.

2 ? 60 ? 60 = 2 * 3,600 = 7,200 seconds

Answer: C

Remember: the unit that you are trying to cancel is placed on the opposite side of the conversion factor. The example above started with hours in the numerator, so hours was placed in the denominator of the first conversion factor.

Since converting between hours and seconds is so common on the GMAT, it is useful to memorize the conversion factor that will allow you to do this calculation in one step:

1 hour = 3,600 seconds

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In the preceding examples, we began with an amount: 46 kilometers in the first example, and 2 hours in the second example. In many cases, we will actually begin with a ratio. Example 3. A car is travelling at 45 miles per hour. What is its speed in meters per second? (1 mile = 1.6 kilometer, 1 kilometer = 1,000 meters) (A) 20 (B) 25 (C) 30 (D) 36 (E) 72

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Solution: You can do this problem in two steps. First, convert miles/hour to meters/hour:

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?

?

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= 45 ? 1.6 ? 1,000 = 72,000 meters/hour

Then, convert meters/hour to meters/second:

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?

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=

=

= 20 meters/second

Note that this entire conversion could have been set up in one calculation:

?

?

?

?

=

=

=

20 meters/s Answer: A

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