Fractions and Decimals

Decimal Numbers

Did you know that the Indian mathematician Aryabhatta was the father of modern numeral system? There are different types of numbers that exist in this number system. In this discussion, we shall look at the concept of decimal point and numbers to understand their importance and significance with solved examples.

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What are Decimal Numbers?

We know the different types of number systems like natural numbers (1,2,3….), whole numbers (0,1,2,3….) and integers (….-2,-1,0,1,2……) used in mathematical expressions. Integers also consist of fractions like 3/5, 9/2 etc. Well, the decimal numbers are actually a type of fractions.

As the name implies (Greek: Deca = 10) decimal numbers are fractions with the divisor as 10 or multiples of 10. A unit is represented as 1. If I ask you to divide 1 into 10 equal parts then each part is called one-tenth of the original,

  • One tenth is 1 unit divided into 10 equal parts = 1/10
  • Similarly, One hundredth is 1 unit divided into 100 equal parts = 1/100
  • One thousandth is 1 unit divided into 1000 equal parts = 1/1000

and so on as the value of the divisor increases the output gets smaller and smaller.

Decimal Point

Decimal Point

The decimal point is the most important concept here. This point is used to denote the number has been divided by 10 or its multiples. For example,

  • 1/10= .1  (read as point one)
  • 1/100 = .01 (read as point zero one)
  • 1/1000=.001 (read as point zero zero one)

thus 377/1000=.377 (read as point three seven seven) and  12966/100=129.66 (read as one hundred and twenty-nine point six six). The number placed to the left of the decimal point is larger than one and the number placed to the right is less than one.

The decimal point is placed to the right of the unit’s place in the number. This point makes it easy to read and represent a number or fraction. For example, 978/1000 can be easily represented as 0.978 and instead of reading nine hundred and seventy-eight divided by one thousand we can read it as point nine seven eight without changing its meaning.

Representation

To represent a decimal fraction with a decimal point consider the unit place of the dividend or the numerator. Count the number of zeroes in the denominator and then moving left from the unit place of the numerator place the point after an equal number of digits.

For example, consider the fraction  2489/100. Here the number of zeroes in the denominator is 2. So moving left from the unit place of the numerator we place the point after 2 digits i.e. left of 9 and 8. So, 2489/100=24.89 (read as twenty-four point eight nine).

Consider the fraction 3/1000. Here the denominator has 3 zeroes. But in the numerator, we have only the unit place. In such a case from the unit place, we move 3 places left using zeroes ahead of the numerator. So, taking the unit place and moving left we cover 1 point, then we add one zero and cover 2 points, again we add one more zero and thus cover 3 points.

So, 3/1000=.003 (read as point zero zero three). Let’s take a look at some of the mathematical operations using decimal numbers.

Addition

Addition of decimal numbers follows the same rules as the addition of integers. Make sure to put the decimal point at the required location. For example, 273.05+ 21.705= 294.755

Subtraction

Rules of subtracting decimal numbers are the same as that of subtracting integers. Make sure to put the decimal point at the correct location. For example, 273.05-21.30=251.75

The topics of multiplication and division of decimal numbers have been dealt with in another discussion.

Solved Question For You

Question 1: The sum of two numbers is 31.021. If one of them is 11.56,  then the other number is

  1. 19.461
  2. 17.461
  3. 18.461
  4. 19.561

Answer : A. 31.021 – 11.56 = 19.461

Question 2: What is a decimal number called?

Answer: A decimal fraction, which we also call a decimal, refers to a number having a decimal point in it. For instance, 2.34. Then we look at the “decimal part” of a number that in fact means the fractional part, the non-whole part.

Question 3: What is a decimal point used for?

Answer: A point which is a small dot that we use to separate the whole number part from the fractional part of a number. For instance, in the number 45.8, the point separates the 45 which is the whole number part from the 8 that is the fractional part, which actually means 8 tenths.

Question 4: Is a decimal an integer?

Answer: We can express every integer as a decimal, however, do remember that most numbers which we express as a decimal are not integers. Thus, if all the digits after the decimal point are zeroes, the number will be an integer. If there are any non-zero digits after the decimal point, the number will not be an integer.

Question 5: How do we subtract decimals?

Answer: In order to subtract decimals, we should note that it is not as same when we subtract integers. Thus, remember to put the decimal point in the correct position. For instance, 283.05-22.30 = 260.75.

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