What are Decimals? The decimal number system is most commonly used for representing a number that is either fraction or not whole numbers. For example; in 4.15, 0.15 is known as decimals, 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,….., etc. but to reduce complexity decimal is dropped from the whole numbers.

The representation of decimal number system uses the powers of 10 for representing the numbers. The value of its place of each digit resembles 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 place

1 is holding the place of tens

And 2 is at the ones or units place.

Whereas, for digits after the decimal;

2 is holding the tenths place

1 is at the hundredths place

0 is in the thousandths place.

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

\( 8 (1000) + 6 (100) + 1(10) + 2(1) + 2(\frac{1}{10}) + 1(\frac{1}{100}) + 0(\frac{1}{1000})\)## Addition and Subtraction of Decimals

If you want to perform addition or subtraction on 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.

**Question 1:** What will be the sum of 4,268.987, 23.45 & -67.89

**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; 4,268.987 + 0023.450 + (-0067.890) = 4,224.547

## Multiplication of Decimals

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

**Question 2:** Calculate the value of 25.85×7.268

**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 7.268 also the decimal places=3. Total=5

So, the solution is 187.87780

Let’s solve a few problems and be completely ready to tackle GRE questions.

## Decimals in Scientific Notation

**Question 3:** 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 negative exponent. So, our answer will be 7.005 × 10-5.

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