Decimals

Decimal are important in our daily life to deal with money, weight, length etc. Decimal numbers are important where more precision is required than the whole numbers or integer. For example, when we calculate human weight on the weighing machine, weight does not always find equal to a whole number on the scale. As we know gold is very valuable so when we weight gold one milligram also countable. So we calculate the cost of the gold even for milligram. This case decimals are important. weight vegetables ect….

Impotence of  Decimals

Here is and example…

let us Take a scale, you can see those small lines in between  two centimeters. Same for any two numbers.

    |      |           |          |          |          |           |         |         |           |       |

    1     1.1   1.2      1.3  1.4    1.5    1.6   1.7   1.8    1.9   2

There is a way of writing A decimal…

Decimal places

 On the Integer part we have places …TH(thousands) H (hundreds) T(tens) O(ones) we read the integer places right to left. Like that We have places for  the decimal part too, and we read the decimal places left to right.

If you have Wondered why the decimal part does not have the ones place in the above diagram, there is a reason. Because ones is already been declared in the integer part ,so we must start as     t-tenths, h-hundredths, th-thousandths  (represent as small letters).

Remember that read out a decimal part numbers individually. Ex. Eight hundred and fifty point zero six eight.

Like and unlike decimals

Just like, unlike and like fractions we have like and unlike decimals.  we can say if a decimal is unlike or like when we compare more than 1 decimal. Like decimals are when the digits in the decimal part are equal. Unlike decimals are when the digits in the  decimal art are not equal.

Converting unlike decimals into like decimals

• Take the  largest decimal place number.
• Then check how many digits are there in the number.
• And then add those Many 0 s to the other number digits.

Here in the above example 8.5801 has 4 decimal places whereas 2.5 has one decimal place so, we add 3 more zeros. Now 2.5 is 2.5000, check 8.5801 and 2.5000 have same number of decimal places. Similarly for 1.50 has 2 decimal places so we add 2 more zeros to 1.50. Again like 2.5 became 2.5000 now 1.50 becomes 1.5000.
Note: adding of zeros end of the number will not change the value of number.

Converting fractions, integers & mixed fractions into decimals

There are 4 ways to convert into a decimal.

1. Integer conversion.
2. Fraction conversion.
3. Mixed fraction conversion. 

 integer conversion:

 

Convert 56 into decimal number. You must add an .0 after the integer 

Fraction conversion:

 Convert 4/8 into decimal number.

1. First  divide the fraction ( 4/8  )
2. Then you will see that the quotient is a decimal. ( 0.5 )

Division:

Here are the steps for division…

1. First, we compare if the divisor > first number dividend.
2. If divisor is greater than first number dividend combine the second number and check with the divisor and ,so on
    (if there are numbers after the first number.)
3. If  the divisor > dividend and, if no numbers after the first number of dividend, add a ‘ 0 .’in the quotient.
4. In the example above there is no number after the 4 in the dividend place, and the divisor (8) is greater than the dividend so we add a 0 because 8×0=0 and 0 is less than 4. than do the division process.
5. Usually there should be  ‘.0000…’ after the dividend so (having .00… wont change value) .
6. To complete the division process we bring a number down to the difference (4). There is  point after dividend (4 as mention in point 5), so we push the point up in to the quotient place and we push down a zero after the decimal part. So if the dividend is smaller than the divisor we have unlimited zeros to push down.
7. Now we can continue division process.

Mixed fractions

A Mixed Fraction is a whole number and a proper fraction combined.

How to covert mixed fraction to fraction

Here before we convert a mixed fraction into a decimal,

we need to convert it into a fraction.

Here is how…

1. First multiply the integer with the denominator.
2. Then add the product with the numerator.
3. Then  the original denominator will be the same for the denominator ,and the product of the of the
   integer × denominator + original numerator will be the numerator ●

In the above example,  we multiplying the 6 with the denominator 2 and adding the product 12 with  the numerator 3. Now we have  15/2 which is the converted fraction.
Remember that all mixed fractions are improper fractions.

Converting mixed fraction into decimal

As mentioned, in slide no.10 divide the fraction to get the decimal.

Converting a decimal into a fraction

Convert 0.62  a fraction.

First check how many decimal places are there in the decimal part.
ex.  0.62/1 then multiply it by  numerator and denominator with 10 powers equaling the number of decimal places.
In the given example, the number of decimal places are 2.
So we have to multiply with 10^2 (100) in the numerator and denominator.   (0.62×100)/(1×100)

then your answer will be 62/100

try to simplify the fraction more divide the fraction with the numerator and denominator highest common factor.

So the answer is  31/50  .

Converting  an improper fraction into a mixed fraction

 

Let us say that we’ve a fraction as 8/7  it is an improper fraction, to make it a proper fraction, we need to  convert into a mixed fraction.

 so here is how we do it.

 First, we divide the fraction like normal division 8÷7.

Quotient =1,Reminder=1

Then the quotient is the integer, the divisior is the denominator and the reminder is the numerator,

 so the mixed fraction is… 1 1/7

• Note: there are 2 pizzas each divided in to 6 slices. One person first had all the six slices of 1 pizza, and then  second person had 1 slice out of the six from the second pizza.
• So, the total pizza eaten is ⁷⁄₆ slices of pizza. And that’s an improper fraction with a numerator greater than the denominators

Decimal operations

Just like we have operations addition +, subtraction -, multiplication × and division ÷ .

We can do it for decimals too.

Decimal Addition:

Decimal addition is so like normal addition just place the two number on their respective places  60.32 + 69.89

perform the addition from right to left including the decimal places.

After adding numbers, count the highest decimal places in given numbers. Then  count  from right to left in addition value and place a decimal point .
Given example highest decimal places are 2, so count the 2 pleases from right to left in addition value and place the decimal point.

Decimal subtraction:

Decimal subtraction is similar as normal subtraction , just place the two number on their respective places

69.32-68.89

perform the subtraction from right to left including the decimal places.

After subtracting numbers, count the highest decimal places in given numbers. Then  count  from right to left in subtracted value and place a decimal point .
Given example highest decimal places are 2, so count the 2 pleases from right to left in subtraction  value and place the decimal point

Decimal Multiplication:

Decimal multiplication similarly  as normal multiplication,
There are 3 types of multiplication .

• •Ignore decimal point when doing multiplication (with one integer and one decimal/both decimal number multiplication)
• power of then multiplication

Power f ten multiplication:

Here you move the decimal point to the right equaling number of zeros in the power of ten.

Decimal point multiplication (one decimal and one integer):

 

If you have one integer and one decimal remove the decimal point from the decimal, then multiply it like normal multiplication. Then after you get the answer check how many decimal places you have in the decimal number , add decimal point after those many number(count from right to left).

Ex: 8.5×4 remove decimal point and do normal multiplication.  Here after one number decimal point is there so add decimal point after one number in value of the multiplication.

Decimal point multiplication (both decimal number):

If you have two  decimals to multiply then, two remove the decimal point from the both decimals, then multiply it like normal multiplication. Check how many decimal places are there  in the both decimals number then  sum the decimal places  and add those places many places  in multiplication value(count and add from right). Ex: 3.58 x 5.8. remove the decimal point and do multiplication. In the multiplication value add decimal point after 3 places.

Decimal division:

What if we needed to divide with an integer on the divisior and dividend as decimal. we need to remove the decimal point and do normal division. Then in the quotient add decimal point after those many number (count and add from right to left).

Ex: 9.6 ÷ 6

Decimal division (divisor as decimal):

What is the divisor is a decimal here is what you must do is multiply it by  power of ten then do normal division. After count the decimal places and add decimal point in the quotient.