Decimal Numbers

Decimals:
The Number system that we follow is called base 10 number system. In this system, we have numbers between 0 and 9, which defines every other number.  Fractional part of a number can be expressed as decimals.
What is a decimal?
Decimal is way of representing a fraction without numerator and denominator. The period or decimal point signifies that the number following it is fractional part. Decimal number can be either greater than or lesser than one. In case of decimal numbers, which are less than one, the leading number is zero.
Example:
39/10 = 3.9 [Decimal number greater than one]
79/100 = 0.79 [Decimal number less than one]
Decimal Place value:
In numbers, position of a number decides its value.
For example in counting number 345, the 3 represents three hundreds, 4 represents four tens and 5 represents 5 units. Similarly, in decimal numbers also, we have place value
Naming decimals:
One tenths = 1/10
One hundredths = 1/100
In 0.7, there are seven tenths.
In 0.79, there are seventy nine hundredths
In 0.798, there are seven hundred and ninety eight thousandths.
Decimal to fraction:
Let us learn how to convert a decimal into fraction.
Step 1: Find the number digits after the decimal point
Step 2: Write the number without the decimal point in the numerator
Step 3: in denominator write 1, followed by as many zeros as the number of digits after the decimal point in the given number
Example: Convert 0.347 into a fraction
Step 1: Number of digits after the decimal point is 3
Step 2: Numerator = 347
Step 3: Denominator = 1000
Hence, the fraction is 347/1000
Decimal to percent:
Let us learn how to convert a decimal number into a percentage.
To convert decimal to percent, multiply the decimal number by 100 and add % sign.
In other words, shift the decimal point to the right and add % sign.
Example: Convert 0.95 into percentage.
0.95 x 100 = 95%
Convert 0.895 into percentage.
0.895 x 100 = 89.5%
Rounding decimals:
Reducing the number of digits without any appreciable change in its value is called Rounding off.  You need to know how many digits you would like to have after the decimal point to round off.
It involves two steps.
Step 1: Decide the number of digits that want to keep in a decimal number.
Step 2: Increase by 1 if the next digit is greater than or equal to 5.
Step 3: Leave it, as it is if the next digit is less than 5.
Example:
Round off 0.789 to nearest hundredths.
0.789 is rounded off to 0.79, as the next digit 9 is greater than 5.
Round off 0.5674 to nearest thousandths.
0.5674 is rounded off to 0.567, as the next digit 4 is less than 5.

Measures of Central Tendency

Central Tendency is one of the main topics of statistics. There are three measures of statistics central tendency. The three measures of central tendency are mentioned bellow:

• Mean
• Median
• Mode

There are again three different types of mean: arithmetic mean, geometric mean and harmonic mean.

Next time i will help you with inference statistics. Till then understand this concept better. For more help you can connect with an online tutor and get your required help. Not just statistics, but you can get help from a trig tutor for trigonometry concepts.

Do post your comments.

Units of time

Let us learn about Units of time

• Milliseconds, Minutes, Nanoseconds, Picoseconds
• Seconds, Weeks, Attoseconds, Centiseconds, Centuries
• Deciseconds, Days, Microsecond, Hours
• Leap year, Year, Yoctoseconds
• Millennia, Femtoseconds

Time is very precious especially to students. Time has been referred as the continuum in which events occur in succession from the past to the present and on to the future

In our next blog we shall learn about density altitude calculator I hope the above explanation was useful.Keep reading and leave your comments.

If you are interested to learn English Tenses, you can click on given link.

easy general knowledge questions

Let us try to find answers for easy general knowledge questions

1) what is 55-17?

2) What number is 75% of 4?

3) A triangle with 2 equal sides is what kind of triangle?

4) Is this true, all Real Numbers belong to Complex Numbers?

5) The product of 2 fractions is 5. If 1 of them is the mixed number 61/5, what is the other number?

In our next blog we shall learn about properties of covalent compounds I hope the above explanation was useful.Keep reading and leave your comments.

composite number chart

Let us learn about composite number chart

A composite number has factors in addition to 1 and itself. All numbers which end in 5 are divisible by 5. Hence all numbers which end with 5 & are greater than 5 are composite numbers.

A number is known as "composite" if it can be divided evenly into 2 or more parts. In other words, it is a positive integer which is divisible by numbers other than 1 & itself. The smallest composite number is four. The 1st few composite numbers are as follows: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21...... A composite number is "an integer that is exactly divisible by at least 1 positive integer other than both itself and 1. All numbers are divisible by both one & itself. That is, a number which has more than 2 divisors other than 1 & the number itself is known a composite number.

In our next blog we shall learn about cost of sales formula I hope the above explanation was useful.Keep reading and leave your comments.

quantitative variables

Let us learn about quantitative variables

Measure the variable by a number is known as quantitative variable. The numeric values are known as variable. Quantitative variables are always ordered values, interval sequence & ratio scales.

Distributions of quantitative variables are represented by dot plots, histogram, box plots & scatter plots. Quantitative variables are always discrete & continuous variables.

In our next blog we shall learn about properties of alkali metals I hope the above explanation was useful.Keep reading and leave your comments.

integration by partial fractions

Let us learn about integration by partial fractions

If the integrand is in the form of an algebraic fraction & the integral cannot be evaluated by simple methods, the fraction requires to be expressed in partial fractions before integration takes place.

We decompose fractions into partial fractions like this due it makes certain integrals much easier to do, & it is applied in the Laplace transform, which we meet later.

Evaluate ∫ (x² + 1) / (x² -5x + 6) dx.

The integration by partial fractions is not a proper rational function on dividing

(x² + 1) by (x² - 5x + 6), we get

(x² + 1) / (x² - 5x + 6) =1 + (5x - 5) / (x² -5x + 6) =1 + (5x -5) / (x - 2) (x - 3)

Now, let (5x - 5) / ( x - 2)(x - 3) = A / ( x -2) + B / ( x -3)

=> (5x - 5) / (x - 2) (x -3) = A(x -3) + B(x -2) / (x -2) (x -3)

Placing x =2 on both sides of (i), we get A = -5

Placing x =3 on both sides of (i), we get B =10

( x² + 1) / (x² - 5x +6) =1 - 5 / (x -2) + 10 / (x -3)

=> ∫ (x² + 1) / (x² -5x + 6)dx = ∫ dx - 5 ∫ dx / (x - 2) + 10 ∫ dx / (x -3)

= x -5 log | x -2 | + 10 log | x -3 | + C

In our next blog we shall learn about extraction of aluminium I hope the above explanation was useful.Keep reading and leave your comments.