GMAT Math : Understanding decimals
Study concepts, example questions & explanations for GMAT Math
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Example Questions
Example Question #1 : Understanding Decimals
Rewrite as a fraction in lowest terms:
Example Question #1 : Understanding Decimals
Add one hundred seven ten-thousandths to seventeeen one-hundredths.
Two hundred seventy-seven one-thousandths
One thousand one hundred seventy-seven ten-thousandths
One thousand seven hundred seventeen ten-thousandths
One thousand eight hundred seven ten-thousandths
One hundred eighty-seven one-thousandths
One thousand eight hundred seven ten-thousandths
One hundred seven ten-thousandths = 0.0107
Seventeeen one-hundredths = 0.17, or 0.1700
The sum:
This is one thousand eight hundred seven ten-thousandths.
Example Question #1 : Understanding Decimals
Multiply seventy-seven one-hundredths by sixty-six one-thousandths.
Forty-six thousand six hundred sixty-two hundred-thousandths
Five thousand eighty-two ten-thousandths
Five thousand eighty-two hundred-thousandths
Five hundred eighty-two ten-thousandths
Five hundred eighty-two hundred-thousandths
Five thousand eighty-two hundred-thousandths
Seventy-seven one-hundredths = 0.77
Sixty-six one-thousandths = 0.066
The product:
0.77 and 0.066 have a total of five digits to the right of their decimal points, so position the decimal point in the answer so that there are five digits to its right.
This is five thousand eighty-two hundred-thousandths.
Example Question #1 : Understanding Decimals
Divide eight hundred eighty-eight thousandths by sixty-four ten-thousandths.
Eight hundred eighty-eight thousandths = 0.888
Sixty-four ten-thousandths = 0.0064
Set up a long division:
Move the decimal point four places right in both numbers so that the divisor will be a whole number. Note that this will require the use of placeholder zeroes in the dividend.
(Note that leading zeroes have been removed.)
Carry out the long division, making sure you align the decimals:
The quotient of this division is that of the original problem, so the correct choice is 138.75.
Example Question #2 : Understanding Decimals
Which of the following is the square of twenty seven one-thousandths?
The correct answer is not among the other responses.
Seven hundred twenty-nine one-millionths
Seven hundred twenty-nine one-hundred-thousandths
Fifty-four one-hundred-thousandths
Fifty-four one-millionths
Seven hundred twenty-nine one-millionths
Twenty-seven one-thousandths = 0.027
Its square is
Multiply without regard to the decimals first:
0.027 and 0.027 have a total of six digits to the right of their decimal points, so position the decimal point in the answer so that there are six digits to its right.
This is seven hundred twenty-nine one-millionths.
Example Question #2 : Decimals
Which of the following is the cube of fifteen one-hundredths?
Three thousand three hundred seventy-five one-millionths
Forty-five one-millionths
The correct answer is not among the other responses.
Three thousand three hundred seventy-five one-hundred-thousandths
Forty-five one-hundred-thousandths
Three thousand three hundred seventy-five one-millionths
Fifteen one-hundredths = 0.15
Its cube is
Multiply without regard to the decimals first:
0.15, 0.15, and 0.15 have a total of six digits to the right of their decimal points, so position the decimal point in the answer so that there are six digits to its right.
This is three thousand three hundred seventy-five one-millionths.
Example Question #3 : Understanding Decimals
Subtract nine hundred six ten-thousandths from four tenths.
Three hundred ninety-four thousandths
Three thousand ninety-four ten-thousandths
Three hundred ninety-four ten-thousandths
Three thousand nine hundred four ten-thousandths
Five hundred six thousandths
Three thousand ninety-four ten-thousandths
Nine hundred six ten-thousandths = 0.0906
Four tenths = 0.4, or 0.4000
The difference:
This is three thousand ninety-four ten-thousandths.
Example Question #2 : Understanding Decimals
Which of these equations is not correct?
Although tempting, a calculator is not required to spot the correct answer.
Example Question #3 : Decimals
If we divide 10 by 3, what is the 10th digit after the decimal point of the quotient?
The tenth digit after the decimal point is 3.
When dividing 1 by 3 or 10 by 3, we get repeating 3s. So, there must be a 3 in the tenths digit.
Example Question #1 : Understanding Decimals
If 
Given that
it follows that 
We don't need to know 
Where the remainder is any one of the answer choices. This is because the remainder for any divisor/dividend pair is the product of the decimal portion of the quotient and the divisor.
Since we don't know y, our answer choice for the remainder is any answer that satisfies the above equation for a positive interger, since 
The only answer choice that satisfies the constraints on 
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