Table of Contents
- Introduction
- Rounding Decimals
- Decimal Addition / Subtraction
- Decimal Multiplication / Division
- Decimals and Powers of Ten
- Decimal Approximation
- How to Find the Unit’s Digit
Introduction
A decimal is a linear array of digits that represents a real number; every decimal place indicates a multiple of a negative power of 10.
Examples include:
-3.11, -0.33, 0.33, 3.11
Note the position of the decimals and the names of their corresponding power of 10.
It is common for the GMAT to ask you to solve a number properties problem, while providing a little bit of information, such as the position of the decimal. Most students in their haste to complete the section within the allotted time, will quickly glance at this problem and immediately try to find the solution.
However, as you may have noticed, many of the decimal place names sounds very similar to each other
… For example, hundred and hundredths, these two powers differ by only three letters in name yet completely change the outcome of a solution because they are on opposite sides of the decimal point.
An extremely common mistake is to misread the wording on the problem and to put the decimal point in the wrong place. The GMAT knows this is a common mistake, and 99% of the time, a solution with this mis-interpretation will be present as one of the answer choices.
Watch out for this trap! Every time you see a statement citing a decimal, look at the end of the word and see if there are any –ths, which indicate that the digit is to the right of the decimal. Once you ascertain this truth, write the number down so that you will not become confused.
Rounding Decimals
Rounding
The GMAT follows normal rounding convention. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
28 rounded to the nearest ten is 30
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
23 rounded to the nearest ten is 20
Decimal Addition / Subtraction
Decimals can only be added / subtracted when they are lined up accordingly.
This is a simple rule but one oft forgotten amidst hasty calculations. Don’t make the mistake of being lazy; always line up your decimal points when performing calculations.
Decimal Multiplication / Division
To multiply decimals: sum the number of decimal places in both numbers, multiply the numbers like normal, obtain the product and position the decimal point n spaces to the left of the last digit, where n is equal to the sum of the number of decimal places in both numbers.
Example
To divide decimals: multiply both numbers by the logical power of ten to get rid of the decimal. Divide as normal.
Example
Decimals and Powers of Ten
Anytime you multiply for 10, shift the decimal to the right. Anytime you divide by 10, shift the decimal one place to the left.
Decimal Approximation
Problems that involve manipulating unwieldy, complex numbers can simplified by rounding to the nearest logical whole number. If a problem looks like it will require too much detailed computation, take a look at the answer choices. Chances are good that you can use rounding to save time.
Example
Always be on the lookout for time saving shortcuts that can be implemented during the test. Certain problems are designed to challenge the test takers decision making skills. If the problem has the keyword “approximate” or looks overly complex, glance at the solution choices. Chances are good the answer choices will involve nice simple numbers, and you need to approximate to solve the question within a reasonable time frame.
How to Find the Unit’s Digit
To find the last digit of a number in a multiplication problem such as the one seen below: work out the exponent for each base number, take the unit’s digit of all the base numbers and multiply them together. The resulting number’s unit digit is the answer.
Example
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