Operations on Decimals

Decimals:
Numbers representing fractions without having any numerator or denominator is called a decimal number.
Example: 0.567, 0.2, 0.49
Decimal Chart:
The value of a number in a decimal is decided by its place value.
0.345
3 represents three tenths = 3/10
4 represents four hundredths = 4/100
5 represents five thousandths = 5/1000

In engineering calculations, fractions are used extensively. As we know that, we can always express a fraction in terms of its corresponding decimal number. We have a ready reckoner that gives us corresponding converted values of a fraction.
1/64   = .015625 1/32   = .03125 3/64  = .046875 1/16 = .0625
5/64   = .078125 3/32   = .09375 7/64  = .109375 1/8  = .125
9/64   = .140625 5/32   = .15625 11/64 = .171875 3/16 = .1875
13/64   = .203125 7/32   = .21875 15/64 = .234375 1/4  = .25
17/64   = .265625 9/32   = .28125 19/64 = .296875 5/16 = .3125
21/64   = .328125 11/32  = .34375 23/64 = .359375 3/8  = .375
25/64   = .390625 13/32  = .40625 27/64 = .421875 7/16 = .4375
29/64   = .453125 15/32  = .46875 31/64 = .484375 1/2  = .5
33/64   = .515625 17/32  = .53125 35/64 = .546875 9/16 = .5625
37/64   = .578125 19/32  = .59375 39/64 = .609375 5/8  = .625
41/64   = .640625 21/32  = .65625 43/64 = .671875 11/16= .6875
45/64   = .703125 23/32  = .71875 47/64 = .734375 3/4  = .75
49/64   = .765625 25/32  = .78125 51/64 = .796875 13/16= .8125
53/64   = .828125 27/32  = .84375 55/64 = .859375 7/8  = .875
57/64   = .890625 29/32  = .90625 59/64 = .921875 15/16= .9375
61/64   = .953125 31/32  = .96875 63/64 = .984375

Multiplying decimals
In multiplication of decimal numbers, we follow two steps:
Step 1: Multiply the numbers without taking into consideration of decimal points
Step 2: Place the decimal point starting from right and moving as many digits as the sum of the number of digits in decimal part in both numbers towards left.
Example:


Dividing decimals:
We have two steps to follow.
Step 1: Convert both numerator and denominator into fractions
Step 2:  Follow the rules of division of fractions.
Example: 14.4 ?0.12
Step 1: 14.4 = 144/10 and 0.12 = 12/100
Step 2: 144/ 10 ? 12/100 = 144/10 ?100/12 = 120
Subtracting decimals:
To subtract decimals one from the other we follow
Step 1: Write the numbers one below the other with decimal point coinciding
Step 2: Add zeros to make length of the numbers same
Step 3: Follow the laws of subtraction to subtract
Example:
0.56- 0.287
0.560
0.287
-------
0.213
Terminating decimals:
The word terminate means end. A decimal number with definite number of digits (ending) is called terminating decimal.
Example: 0.495. There are three digits after the decimal point.
All terminating decimals can be represented as a rational number.
Dewey Decimal System:
In public libraries, books are catalogued according to the subjects. Dewey Decimal System (DDC) is the most widely used system of classification for organizing books in libraries. In this system, integer part of the number gives us the specific subject and decimal part gives us the specific part of the subject.
For example:
In DDC, 512.12 represents a book on Algebra, 815.4 represents a book on 16th century Italian poetry.

Exponents and their rules

Fractional exponent is also called as a rational exponent which is in the form of a fraction like ½ (square root), ⅓ (cube root), ¼ (fourth root) etc.

A fractional exponent with 1/n is the n-th root of the given base.

(a)^ ⅓ = ³√a

A fractional exponent with m/n, we need to take the m-th power of the base and then find the n-th root or vice versa

(a) ^⅔ = ³√a²

The basic exponential rules are as follows: 

Exponents and tLaw of exponents:

1. Any number except zero when raised to zero equals 1
2. Any number raised to 1 equals itself
3. A number with negative power equals its reciprocal with a positive power
4. When we divide terms with same bases, the powers are subtracted
5. When we multiply terms with same bases, the powers are added
6. When a term is raised to a power with a whole power, the powers are multiplied.
7. When product of terms are raised to a power, each term is raised to that power

Subtracting exponents:

When we divide terms with same bases, the exponents are subtracted

The basic exponential rules are as follows: 

For example,

= 3³

Exponent rules:

1. When we multiply terms with same bases, the powers are added

2. When we divide terms with same bases, the powers are subtracted

3. Any number except zero when raised to zero equals 1

4. Any number raised to 1 equals itself

5. When a term is raised to a power with a whole power, the powers are multiplied.

6. When product of terms are raised to a power, each term is raised to that power

7. A number with negative power equals its reciprocal with a positive power

LESSON ON VOLUME OF SOLIDS

Often, students work with shapes and solids under Geometry. Geometry deals with the study of solids and shapes and the measurements associated with them. Therefore various calculations with respect to the size, shape and volume is often done under Geometry. One of such computations is calculating volume of solids.
There are various types of solids. They are:

· Cube

· Cuboid

· Prism

· Pyramid

· Cylinder

· Sphere

· Cone

Students can use various volume formulas to calculate the volume of the various solids. The Volume is basically the 3 dimensional 'space' occupied by a particular solid.

Students can solve problems on finding volume and learn how to find volume of various solids. Ample problems are available online for students to practice upon. They can also get Geometry tutoring online to get help with solving problems in geometry.

how to find the slope

Let us learn how to find the slope

Interpret the slopes of the following lines joining

(i) (6,4) and (−7, 4) (ii) (−2,8) and (−2, 7).

(i) To find Slope of the given line “m”= y₂- y₁ / x₂ – x₁ = 4-4 / -7- 6 = 0 /-13 = 0

∴ Therefore line is parallel to the x-axis.

(ii) To find Slope of the given line “m” = y₂- y₁ / x₂ – x₁ = 7-8 / -2+2 = not defined.

Therefore, The line is perpendicular to the x-axis.

In our next blog we shall learn about blood type personality traits I hope the above explanation was useful.Keep reading and leave your comments.

Do you like to speak English? Do You Speak English? click on the given link to learn English.

final exam calculator

Let us learn about final exam calculator

Final exam score is referred as the calculation of the marks secured by each student that can be used to predict the results of the students & the grades secured by them.
Final exam score includes calculation of the total marks of students, calculation of the percentages & the final step is the prediction of the grade with respect to his/her percentage.
Final exam score calculator is mostly used in the educational institutions to predict the grading of their students & the grading system often requires the final percentage of score of the students. Final exam calculator helps tutors to calculate score which helps the institutions to know the ranking of their university according to their pass percentage of the students.

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

standard deviation table

Let us learn about standard deviation table

Standard deviation table, a standard normal table also known as the "Unit Normal Table" is a math table for the values of Φ, the cumulative distribution function of the normal distribution. Standard deviation table are used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution, & by extension, any normal distribution.

Standard deviation table is the measure of describing squared mean difference variability & spread of the Data set in the given total numbers. Standard deviation table is used to take the measurement of taking square root and average of numbers in the Data set.

Formula for standard deviation,

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

logarithm solver

Let us solve problem using logarithm solver

Solve for x: 5^x = 2.
Apply the logarithm of both sides.
log 5^x = log 2
Use theorem 2 to simplify the equation.
x * log 2 = log 5
Solve for x by dividing each side by log three
x = (log 5/log 2)
A decimal approximation may be found if desired -
x = 2.32192809.
Solve Log₃(2x+5) = 2 for x.
Write an equivalent exponential expression, 2x+5= 3²
2x+5=3*3
2x+5=9
Solve for x. 2x=4, x = 2.
In our next blog we shall learn about what is naoh I hope the above explanation was useful.Keep reading and leave your comments.

equivalent fractions calculator

Let us solve problem using equivalent fractions calculator

Convert 9.6 to equivalent fraction number by using equivalent fractions calculator
Here transfer 9.6 to an equivalent fraction,
Multiply both the numerator & the denominator by 10.
= (9.6 x 10)/10
= 96/10
Hence there is one digit in a place of the very last digit is the "10th" decimal place. Therefore we can just say that 0.1 is the same as 1/10.
= 9.6 can be written as the equivalent fraction = 96/10

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

maxima and minima

Let us learn about maxima and minima

A function is refers to be monotonic if it is either increasing or decreasing but not both in a given interval.
Consider the function f(x) = 3x+1, x£ [0,1]
The mentioned function is increasing function on R. Hence continuous function is a monotonic function in [0, 1]. Continuous function has its minimum value at x = 0 that is equal to f (0) =1, has a maximum value at x = 1, that is equal to f (1) = 4.
'Every monotonic function imagines its maximum or minimum values at the end points of its domain of definition.'
Point to be remember that 'every continuous function on a closed interval has a maximum and a minimum value
The maxima and minima value of an expression or quantity is meant primarily the "greatest" or "least" value which it can receive. However, there are notes at which its value ceases to increase & begins to decrease; its value at such a point is known a maximum. So there are points at that its value ceases to decrease & begins to increase; such a value is known as a minimum. There may be many maxima or minima, & a minimum is not necessarily less than a maximum. For illustration the expression (x 2 -1x+ 2)/(x - 1) can driven all values from - 00 to - 1 & from + 7 to + oo, but has, so long as x is real, no value between - 1 & + 7. Here - 1 is a maximum value, & + 7 is a minimum value of the expression, though it can be made greater or less than any assignable quantity.
In our next blog we shall learn about interval world I hope the above explanation was useful.Keep reading and leave your comments.

decimal squares

Let us learn about decimal squares Decimal Squares is a program for tutoring place values & the use of decimals. Decimal Squares was improved by Professor Albert Bennett at the University of New Hampshire. The bulk of the program is a series of classroom learning materials & books that are available for purchase. 1 aspect of the Decimal Squares program which you can access for free is the games section.

The games section of Decimal Squares offers 8 interactive games which students can use to develop their understanding of place values.

Decimal Squares are applied as a visual model for the part-to-whole concept of decimals & for illustrating decimal equality, place value, inequality, & estimation.

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

graphing fractions

Let us learn about graphing fractions

The term 'fraction defines a number that is being used to describe a part of a group & while writing it student can use the term denominator & numerator. Nominator is used to write the number that is above the line & denominator is used for the number that is below the line. Best example: If you write the term ½ you can say that the term is being written in terms of fraction & the digit '1' is known as the numerator while '2' is known as denominator.

How to graph fractions on a graph?
The same way student would graph numbers which are not fractions.
SAMPLE:
Graph 1/2 & 3/4 on the real number line.
<------(-2)------(-1)--------(0)------(1)-------(2)---->
Obviously, where would student put fractions 1/2 & 3/4?
The fractions would easily fit between 0 & 1, right?
The same applies to points on a graph.
SAMPLE:
Graph (2, 3/4) & (0, 1/2) on the xy-plane?

How would student graph these points?
For (2, 3/4), student travel 2 units to the right on the x-axis

& 3/4 units UP on the y-axis & plot the point there.
For (0, 1/2), student would NOT travel on the x-axis because of ZERO but student would need to travel 1/2 units UP on the y-axis and plot the point there.

In our next blog we shall learn about earth elements paint I hope the above explanation was useful.Keep reading and leave your comments.

square root of 48

Let us learn about square root of 48

Calculate the square root of 48. Answer: √48= 6.92820323. Factor the radicand & take the square roots of the factors.

√48 = √(16×3)
= √16√3
= 4√3
Simplify the following square root. √48 Solution: √48 = √16*3 = √16 * √3 = √4² √3 = 4√3
In our next blog we shall learn about informal letter I hope the above explanation was useful.Keep reading and leave your comments.

graph quadrants

Let us learn about graph quadrants

There are four quadrants in a graph.
The most used 1 is the first quadrants which is the top right one.
The second quadrant is the 1 on the left of it.
The third is the 1 below the second quadrant
The forth quadrant is the 1 on the graph that is below the first quadrant.

II | I
---+---
III | IV

Divide the graph into four parts & each part is called as quadrant. Traditionally, learner use the x & y axis to divide it. The portion of the graph with positive x & y coordinates is the 1st quadrant; the 2nd has positive y values & negative x values, while the 3rd quadrant has both negative x & negative y values. The last is the 4th quadrants which are below the 1st quadrant. It has positive x values & negative y values.
The point (0,0) the center of a clock, the 1st quadrant is between 3 & 12 & the 2^nd between 12 & 9, the 3rd between 9 & 6 & the 4th between 12 & 3.

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

integral of sin squared x

Let us learn about integral of sin squared x
1st convert sin-squared-x to its double-angle identity: 1/2[1-cos (2x)] & then integrate which expression by conventional process to obtain the solution:
x/2 - sin(2x)/4
The integral of sin x² is one of the Fresnel Integrals. If F(x) = sin x is an function & the derivative of function with respect to x is f(x) = cos x , then we call the integral of f(x) with respect to x is F(x). In trigonometrically term like sin, cos, tan also can be performed in integral calculus.
i.e., ⌡cos x dx = sin x + c, where c is constant.
In our next blog we shall learn about role of students in disaster management I hope the above explanation was useful.Keep reading and leave your comments.

polynomial factor calculator

Let us learn about polynomial factor calculator

Steps to find solution the algebra factoring polynomials calculator are as follows:

* Try to arrange in the order of powers.

* Given expression will be written in standard form ax² + bx + c = 0.

* Try to find the greatest common factor

* Factor any complex variables.

* Try to Solve the terms

x² ( x³+ 5 ) ≡ x²· x³+ x²· 5 ≡ x⁵+ 5x²;
x²( x + 5 ) ≡ x²· x + x²·5 ≡ x³+ 5x²;
x ( x³+ 5 ) ≡ x· x³+ x· 5 ≡ x⁴+ 5x;
x ( x+ 5 ) ≡ x· x+ x· 5≡ x²+ 5x;
here use the identity x ≡ x^1.
In our next blog we shall learn about three parts of cell theory I hope the above explanation was useful.Keep reading and leave your comments.

define function

Let us learn about define function

Functions are what we apply to describe things we want to talk about mathematically.

A function is a bunch of ordered pairs of things with the property which the 1st members of the pairs are all different from 1 another.

Best Example for define function in math:
Suppose the given function f(x) is 8x²+5x+3. Finding the value of f (2)?
Solution: Given function f(x) = 8x²+5x+3
Find the value of f (2)
Substitute the value “x” for 2, then, f (2) = 8x4+5x2+3 =32+10+3, f (2) = 45
In our next blog we shall learn about expected value calculator I hope the above explanation was useful.Keep reading and leave your comments.

mensuration formulas

Let us solve problem on mensuration formulas

Write the given values in a decimal form
a) Six ones and eight- tenth
b) Twenty and six - tenth.
Solution:
a) Six ones and eight- tenth = 6 + 8/10
= 6.8
b) Twenty and six – tenth = 20 + 6/10
= 20.6
Write the following terms in decimal form.
400 + 20 + 8 + 5/10 + 8/100
Solution:
400 + 20 + 8 + 5/10 + 8/100 = 428 + 5 x 1/10 + 8 x 1/100
= 428 + 0.5 + 0.08
= 428.58
In our next blog we shall learn about simplifying radicals calculator I hope the above explanation was useful.Keep reading and leave your comments.

box and whisker plot maker

Let us learn about box and whisker plot maker

Box and whisker plot maker is also called as box plot or Whisker plot. box and whisker plot maker is a suitable way of graphically give a picture of groups of numerical data with the use of their 5-number summaries. Box & Whisker plots are basically applied in the display of statistical analyses of a group of numbers.

A box &whisker graph is applied to display a set of data. hence that you can easily see where most of the numbers are.

The best example, suppose you were to catch & measure: the length of 13 fish in a lake: A box & whisker plot is depend on medians. The 1st step is to rewrite the data in order, from the smallest length to largest: This must be the median middle number because there are 6 numbers on each side.

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

simplify radicals calculator

Let us learn about simplify radicals calculator

Simplify radicals calculator will help to calculate the simplified radical expression of entered values. Simplify radicals calculator will show the work by separating out multiples of the radicand that have integer roots. Simplify radicals calculator Will simplify radical expressions for positive integers for the radical or radicands. Decimals will be rounded down. First we need to find radicands which have whole number roots & pull those outside.
Simplify radicals calculator is able to separate as the release calculator & able to find solution of any rectangle root evens negative ones. Simplify radicals calculator is comparable to solving rational equations, extra than there is 1 other step.
Functions of simplify radicals calculator
The radical functions & standard exponents be capable of separate as the denominator & the numerator of the rational purpose are equivalent trainer & that worth would be x=1.
1. √x + 6 = 10
6 is subtract on both sides
√x + 6 -6 = 10-6
√x = 4
X^2 = 2^2
x=2
2. √x + 21 = 46
21 is subtract on both sides
√x + 21 – 21 = 46 – 21
√x = 25
X^2 = 5^2
x=5
In our next blog we shall learn about percent composition calculator I hope the above explanation was useful.Keep reading and leave your comments.

factors of 56

Let us learn about factors of 56

A factor is a number can evenly be divided into another number. Any number that can be divided by1 & itself. Numbers which can only be divided by 1 & themselves are called prime numbers. The number 1 & the number itself are factors of the number.

Factors of 56 = 2, 4, 7, 14, 28

Divide the given number by first prime number 2.

56/2= 28 remainder is (0).

2 is one of the prime facto

28/2 = 14 remainder (0).

2 is a prime factor.

14/2=7 remainder (0).

2 is a prime factor.

So the prime factor of the number 56 is 2 * 2 * 2 * 7

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

how to divide fractions

In our previous blog we learned how to divide fractions & now let us learn How to divide polynomials

How to divide polynomials can be done by canceling the like terms the following are the steps:
Step 1: Represent the polynomials in division form i.e. numerator and denominator
Step 2: Cancel like terms if any
Step 3: Then divide similar like fractions.
How to divide polynomials x³y² by (x3y)
Given: x³y² and (x³y)
x³y²/(x³y) = y
In our next blog we shall learn about bar graphs I hope the above explanation was useful.Keep reading and leave your comments.

free online tutor

Let us learn about free online tutor

Useful online tutoring links
There many website which allow pupils to brush up on mathematics subject revision methods or to complete their homework. They can also provide tutors & tutoring assistants with various classroom ideas relating to specific mathematics subject topics as well as other subjects in the National Curriculum.

• Revision & homework guides are available here for Key Stages two to AS level students. Learner can take part in practice exercises in subjects like number estimation space, mental arithmetic & measurement & handling data.
• Revision website offers 'bite size' revision guides for pre-schoolers to over-16s. learners can ask the 'SOS' teacher specific mathematics subject questions to help them with their homework.
• These blog resources geared to helping student with their homework problems in mathematics subject & all other curriculum subjects. Games & activities are covered in algebra, geometry, trig & practical science-based mathematics subject starting at Key Stage 1.
• Primary & secondary school students can find mathematics subject revision guides on the Channel 4 bumper website, which also has an 'Ask a question' page, a 'Get an solution' page & a 'Homework High' chat room with a Math zone for interactive role-play adventure games.
• The use of interactive whiteboards, mathematics games, test papers and marking guidelines for teachers are all available at this easy to use site.
• Online exhibition gives children the chance to study confidently, learn about timekeeping & take part in a 'time shuffling' challenge.

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