Decimal in Math Arithmetic

Review ;  Place Value , Decimal to fraction , Addition, Subtraction , Multiplication , Division  of Decimal , Rational and Irrational Numbers

To understand Decimals first we will learn the place values of numbers;

1368 . 597

8  –  Unit place

6  – tens place

3 – One  hundred place

1 –  One Thousand Place

5 – One Tenth Place

9  – One Hundredths Place

7 –  One Thousandths Place

Let us understand the decimals with following example

d2

The number after decimal  is =  742.

The place value of 7 is = 7 x 1/10

4 = 4 x 1/100

2 = 2 x 1/1000

Let us take some more example

Ex.1  –    0.568   = 5/10  + 6/100 + 8 /1000

Ex.2  – 0.0568 = 0/10 + 5/100 + 6/1000 + 8 /10000

Ex.3 –  32.459   = 3 x 10 + 2x 1 + 4/10 + 5/100 + 9/1000

Decimal  To Fraction Conversion  

To convert decimal to fraction just put same number of zeros after 1   in the denominator as the number of digits given after decimal .

  1. 0.1 = 1/10
  2. 6.5 = 65/10
  3. 2.5 = 25/10 =5/2
  4. 5555.55 = 555555/100 = 111111/20
  5. 986.2566 = 9862566/10000

Addition of Decimals;

We can understand addition of decimals like this;

Ex. 4            1256.983  +   0.25

Answer

Now Match the decimal places of numbers precisely and put a ‘0’ to match the digits ; here instead of 0.25 we can write 0.250.

d5

Exercise;

  1. 0.00289 + 1.1
  2. 1.00005 + 0.00069
  3. 987625 + 0.987625
  4. 3658.0256 + 1 .368
  5. 0.011 +0.0003

Subtraction of Decimals

It is same way as normal subtraction; just take care of decimal place of the number.

Example 5                   0.02  –  0.0025

Answer

                     d6

Exercise;

  • 5698.23 – 0.036
  • 75.75 – 75
  • 256896.2568 – 1245.5
  • 0.35 – 0.003
  • 100.245 – 12.689

Multiplication of Decimals

To multiply decimals we should multiply the same way as the whole numbers and then insert decimal according to the number of digits after decimal.

Example 6                   30.05  x  1.5

Answer –        There are two digits after decimal i.e. 0 and 5 in 30.05 and in 1.5   – One digit after decimal  i.e. 5

So, total 2+1 =3 digits after decimal

d7

Put the  decimal before three digits from left , so the answer is 45.075.

OR

Another way to solve this sum is by converting decimals into fraction

3005/100 x  15/10  = 45075/1000 = 45.075

Exercise

  1. 0.01 x 0.02
  2. 56.023 x 1.1
  3. 2645.32 x 52
  4. 0.0005 x 0.01
  5. 897.87 x 45

Division of Decimals

The best way to divide one decimal with another is taking reciprocal inverse of divisor and converts both the numbers (dividend and divisor) into fraction.

Example 7            500.02  ÷  2.02

Answer                        (50002/100)   x   (100/202)

=  247.534653465346

d3

The decimals resulting from lengthy division either terminates or repeats itself .  When the decimal values repeats without ending that time we use a bar above the repeating number; like in example 8 the decimal value 5346 repeating so we can write it like

d4

Terminating Numbers  ;  1/25  = 0.04

50/4 = 12.5

The decimals that terminates or repeats are called as Rational Numbers , While there are some numbers for which decimals do not terminate or repeat like √3 = 1.732050807568………………, π = 3.1428571……….,   and √7 = 2.645751………….  are known as IRRATIONAL NUMBERS.

Exercise

  1.     200  ÷  1.2
  2.     10π  ÷  7
  3.     0.258 ÷ 0.36
  4.    782 . 26  ÷   12.56
  5.     √5 ÷ 5.0

                                                                                        

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