# GRE Quantitative - Arithmetic Decimals

The GRE Quantitative Reasoning section is one of the most important sections in your exam. The decimal number system is most commonly used for representing a number that is neither a fraction nor a whole number. For example; 4.15, .15 is the decimal value, and 4 is the whole number. Hence, it becomes easy to comprehend that any whole number can be expressed in the form of a decimal number. For example, whole number 7 can be represented as 7.0, 7.00, 7.000,â€¦.., etc. but to reduce complexity decimal is dropped from the whole numbers.

The representation of a decimal number system uses the powers of 10 for representing numbers. The value of the place of each digit can be associated with a power of 10. For example, the place value of each digit of the number 8, 612.210 are:

For the numbers before the decimal :

• The place of 8 is thousands
• The place of 6 is hundreds
• The place of 1 is tens
• The place of 2 is ones Â

Whereas, for digits after the decimal :

• 2 holds the tenths place
• 1 holds the hundredths place
• 0 holds thousandths place

In other words, 8, 612.210 can be written as :

8(1,000) + 6(100) + 1(10) + 2(1) + 2 (1/10) + 1(1/100) + 0(1/1000)

## Addition and Subtraction of Decimals:

If you want to perform addition or subtraction of decimal numbers, then line up the decimal points, which you wish to add or subtract and then just perform the desired operations. At some places, you will feel the need to write more zeroes to make the figures of all numbers equivalent.

GRE will ask you such decimal questions which will be a bit complex yet easy to solve in limited time. For example, the sum of 4,268.987, 23.45 & -67.89 is:

Solution: 23.45 can be written as 0023.450 and -67.89 can be rewritten as -0067.890

Now the figures of all three numbers are equivalent. Hence summation becomes easy.

Hence, the solution will be; Â

Â 4,268.987

Â 0,023.450

-0,067.890

Â Â 4,224.547

## Multiplication of two or more decimal numbers:

To multiply decimal numbers, multiply them as you would multiply whole numbers and at the end put the decimal after calculating all decimal places in the actual numbers.

For example; calculate the value of 25.85Ã—7.268

Solution:

• Ignore decimal from both the numbers. So it becomes 2585 and 7268.
• Multiply these two numbers. So, the product will be 18787780
• Calculate total decimal places in the original numbers. So in 25.85, decimal place= 2 and in Â Â Â 7.268 also the decimal places=3. Total=5
• So, the solution is 187.87780

Letâ€™s solve a few problems and be completely ready to tackle GRE questions.

Question: Represent .00007005 in scientific notation.

Solution: To represent a number in its scientific notation, we will need to move the decimal to the place just after the non-zero number. In this question, it is 7, and then we will drop all the non-significant zeros. We will need to move our decimal point five places to the right, and this will give us a negative exponent. So, our answer will be 7.005 Ã— 10-5.

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