Understanding decimals - GMAT Quantitative Reasoning
Card 0 of 10
If 
and 
are positive integers such that 
= 4.46, which of the following numbers could be the remainder when 
is divided by 
?
If
Given that
it follows that 
.
We don't need to know 
or 
, the only important information is that:
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 
is specified as such in the problem.
The only answer choice that satisfies the constraints on 
is 184:
==> 
==> 
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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Rewrite as a fraction in lowest terms: 
Rewrite as a fraction in lowest terms:
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Add one hundred seven ten-thousandths to seventeeen one-hundredths.
Add one hundred seven ten-thousandths to seventeeen one-hundredths.
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.
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.
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Subtract nine hundred six ten-thousandths from four tenths.
Subtract nine hundred six ten-thousandths from four tenths.
Nine hundred six ten-thousandths = 0.0906
Four tenths = 0.4, or 0.4000
The difference:
This is 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.
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Multiply seventy-seven one-hundredths by sixty-six one-thousandths.
Multiply seventy-seven one-hundredths by sixty-six one-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.
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.
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Divide eight hundred eighty-eight thousandths by sixty-four ten-thousandths.
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.
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.
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Which of the following is the square of twenty seven one-thousandths?
Which of the following is the square of twenty seven one-thousandths?
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.
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.
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Which of the following is the cube of fifteen one-hundredths?
Which of the following is the cube of fifteen one-hundredths?
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.
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.
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Which of these equations is not correct?
Which of these equations is not correct?
Although tempting, a calculator is not required to spot the correct answer.
is equal to 
as it is 
parts of 
. And therefore 
must be slightly different. (It's it actually 
)
Although tempting, a calculator is not required to spot the correct answer.
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If we divide 10 by 3, what is the 10th digit after the decimal point of the quotient?
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.
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.
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