Decimals and Place Values

Hello children, let us discuss about decimals in mathematics from CBSE sample papers.

Decimals numbers are commonly used in all walks of our life such as business, medicine, measurement, mass, unit, and currency. (also read on properties of decimal numbers)
Decimals are part of a type of numbers in mathematics called as mixed numbers. A mixed number is combination of whole number and decimal part values.
Place value: The value of a digit is determined by its position in a number which is called place value. Place value is used to indicate the position of number system.
The place values are called as following
1-one
  10 – Ten
  100 – hundred
 1000- Thousands
10000- Ten thousands
100000- hundred Thousands
1000000-million
10000000-ten million
100000000-hundred million
1000000000-billion



Place value of decimal point:
                                                     The following table is representing the place value of decimal point values.

10 = 101 Tens

1 Ones

. Decimal point

1/10 = 10-1 Tenths

1/100 = 10-2 Hundredths

1/1,000=10-3 Thousandths

1/10,000=10-4 Ten thousandths

 Here 10¹ represent the tens place value of whole number system.
10⁰ represent the ones place value of whole number system.
’.’ represents the decimal point number.
10^-1 represents the tenths place value of decimal number system
10^-2 represents hundredths place value of decimal number system
10^-3 represents thousandths place value of decimal number system
10^-4 represents ten thousandths place value of decimal number system.



Let’s see the example: find out decimal point value of this given number 12.768

Sol:  here we have given number 12.768

We start from 1 number
Here 1 represents the type of whole number its place value is tens then original number is 1*10=10
Now start with number 2
Here 2 represent the type of whole number its place value is ones then original number is 2*1=2
Decimal point is separates the whole number.
Third number 7 is represent the type of decimal number and its place value is tenths then original value of 7 is   7*0.1=0.7
Fourth number i6 is represent the type of decimal number and its place value hundredth then the original value of 6 is 6*0.01=0.06
Fifth number 8 is represent the type of decimal number and its place value thousandths then the original value of 8 is 8*0.001=0.008


Let’s see the above example in expanded form:
Sol: given number is 12.768
12.768=    12+ 7/10+6/100+8/1000
So, 12.768 has one tens, two unit, seven tenths, six hundredth, eight thousandths


Let’s see the other example:
Ex: find the place value of this numbers: 456, 0.456,54
Sol:  let‘s see first number: 456
4 numbers is hundred place
         5 number is tens place
      6 ones place

Now we see Second number: 0.456
4 number tenths place
5 number hundred’s place
6 number thousand’s place

See the third number: 54
5 number tens place
4 ones place

In upcoming posts we will discuss about Order of Operations in Grade V. Visit our website for information on algebra help

How to tackle Decimals and Percentage problems?

Previously we have discussed about rational expressions applications word problems and Friends today i am going to teach you one important topic of grade V of karnataka board namely percents and Fractions.A linear array of digits that represents a real number, every decimal place indicating a multiple of a negative power of 10. A number written using the base 10.
For example, the decimal 0.1 = ¹/₁₀, 0.12 = ¹²/₁₀₀, 0.003 = ³/₁₀₀₀

A percent is a ratio whose second term is 100. Percent means parts per hundred. The word comes from the Latin phrase per centum, which means per hundred. In mathematics, we use the symbol % for percent.
Example  of percents
23/100 =23%, 3/100 = 3%
In math fractions, the denominator tells us how many parts the whole is divided into, and the numerator tells us how many of those parts we're dealing with.the number above the bar is called the numerator, and the number below the bar is called the denominator.
Example :  ¾          3 is numerator and 4 is denominator

Every fraction can be converted to a decimal by dividing. If you use the calculator to divide 3 by 4, you'll find that it is equal to 0.75.
Here is a table of commonly occuring values shown in Percent, Decimal and Fraction form:

                                 Percent                   Decimal                  Fraction
                                 1%                                  0.1                     1/100
                                 10%                                0.1                     1/10
                                75%                                 0.75                    3/4

Conversions from Percent to Decimal
Percent-to-decimal conversions are easy; you mostly just move the decimal point two places. The way I keep it straight is to remember that50%, or one-half,. In other words, you have to move the decimal point two places to the left when you convert from a percent (50%) to a decimal (0.50). divide by 100, and remove the "%" sign. (Know more about Percentage ,click here),
Some more examples are
27% = 0.27
104% = 1.04
0.5% = 0.005
To convert from decimal to present in divide by 100, and remove the "%" sign. The easiest way to divide by 100 is to move the decimal point 2 places to the left.
Example
0.123 = 0.123/100 = 12.3
To convert fromFraction to Decimal the easiest way to convert a fraction to a decimal  is to divide the top number by the bottom number (divide the numerator by the denominator in mathematical language)
Example: Convert ²/₅ to a decimal
Divide 2 by 5: 2 ÷ 5 = 0.4
Answer: ²/₅ = 0.4
To  convert a decimal to fraction  needs a little more work.
Example: To convert 0.75 to a fraction
First steps =0.75/1
       ^{=   0.75 × 100}/ _{1 × 100}     Then multiply top and bottom by 10 for every number after the decimal point (10 for 1 number, 100 for 2 numbers, etc)
  = ¾
To convert from fraction to percentage is to divide the top number by the bottom number than multiply the result by 100 and add the % sign,
Example: 38
First divide 3 by 8: 3 ÷ 8 = 0.375,
Then multiply by 100: 0.375 x 100 = 37.5
Add the "%" sign:     and the answer is  37.5%
To convert from percentage to fraction first convert to a decimal (divide by 100), then use the steps for converting decimal to fractions (like above).
Example 80% to convert in fraction
80/100 =0.80
^{0.8 × 10}/ _{1 × 10}   Then multiply top and bottom by 10 for every number after the decimal point (10 for 1 number, 100 for 2 numbers, etc)
And the answer is =8/10 = 4/5
So here we end with Decimals, percents and fractions. I hope that this article will help you in solving problems Decimals, percents and fractions and If anyone wants to know about Percentages in Grade VI and also about LCM, GCF, ratios and proportions then they can refer Internet.

Decimals Percents, and Fractions in Grade V

Hello friends, in this session we are going to learn some topics for grade V students. This article will include the small topics of grade V level like decimals, how to divide decimals,percents and fractions for grade V of west bengal board of primary education.
Now coming to point, the decimals are the type of notation to write numbers in the base ten. It is also referred to as the base ten or the denary number system. We can also say that a decimal number is a type of fraction that has denominator as power of ten, but they are always represented without a denominator term. For example we can take some of the decimal numbers as: 0.56, 0.3564, 10.456, 1.33333, and 243.85 etc.
A decimal always represents the part of a Whole Number and this fraction part of the number starts after the decimal separator or the points between digits so it is also a type of rational number. Sometimes the decimals have some of the repeating digits in the decimal number. For example, 1.788888, 0.1766666, 0.142142142, and 0.01234567 and many more. Now talking about the fraction of a number. The fraction of any number is also represents the part of a whole number but in some other manner. A fraction number shows that how many equal parts are there in any of the integer. In the term of notation of a fraction number, we write one number above another number having a line in between them. The above number is called as the numerator which shows how many parts of the number are there, below number is called as the denominator of the fraction it shows the total number of parts. The separator line shows the fraction of both numbers. For example we can give fraction numbers as ½, ¼, 5/6, 2/3, and 7/4 etc. Fraction is a type of rational number represented in some numerator to the denominator. ¼ shows that 1 part of a number is divided in to four equal parts. So, a decimal, a fraction and a rational number are related to each other and they all represent the same thing but in different manner of notation. For example decimal number 0.5 can be represented as 1/2 as fraction and for more information and example on decimal click here.

The concept of percentage also comes from fraction and decimal numbers. The term percent stands per 100 and represented by the sign “%”. It shows that there is not some part of 100 items or of whole items. For example a basket of fruits having 5 fruits, 3 are apples and 2 are oranges then the percentage of the oranges can be given as 2/5 = 40/100 = 40%, and percentage of apples are 3/5 = 60/100 = 60%. So the percentage is used for the comparison of different numbers, for example we consider the exam result in the form of percentage, profit and losses are considered in the percentage. So we can say that the decimals, percents and fractions are the different ways for showing same value in the number system.
 
The figure shows half of a cake (1/2) as fraction, as decimal 0.5, and as percentage it is 50%.

This is all about the Decimals Percents, and Fractions and if you want to know about Decimals and Place Values and want to Solve Rational Numbers Problem then they can refer to internet and text books for understanding it more precisely.