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Fractions and decimal numbers

A fraction is one number divided by another number. There are several ways to write a number divided by another one, such as a ÷ b , a / b and a b . The first way of writing a fraction is very hard to work with, so we will useonly the other two. We call the number on the top (left) the numerator and the number on the bottom (right) the denominator . For example, in the fraction 1 / 5 or 1 5 , the numerator is 1 and the denominator is 5.

Definition - fraction

The word fraction means part of a whole .

The reciprocal of a fraction is the fraction turned upside down, in other words the numerator becomes the denominator and the denominator becomesthe numerator. So, the reciprocal of 2 3 is 3 2 .

A fraction multiplied by its reciprocal is always equal to 1 and can be written

a b × b a = 1

This is because dividing by a number is the same as multiplying by its reciprocal.

Definition - multiplicative inverse

The reciprocal of a number is also known as the multiplicative inverse.

A decimal number is a number which has an integer part and a fractional part. The integer and the fractional parts are separated by a decimal point , which is written as a comma in South African schools. For example the number 3 14 100 can be written much more neatly as 3 , 14 .

All real numbers can be written as a decimal number. However, some numbers would take a huge amount of paper (and ink) to write out in full! Some decimal numberswill have a number which will repeat itself, such as 0 , 33333 ... where there are an infinite number of 3's. We can write this decimal value by using a dotabove the repeating number, so 0 , 3 ˙ = 0 , 33333 ... . If there are two repeating numbers such as 0 , 121212 ... then you can place dots or a bar, like 0 , 12 ¯ on each of the repeated numbers 0 , 1 ˙ 2 ˙ = 0 , 121212 ... . These kinds of repeating decimals are called recurring decimals .

[link] lists some common fractions and their decimal forms.

Some common fractions and their equivalent decimal forms.
Fraction Decimal Form
1 20 0,05
1 16 0,0625
1 10 0,1
1 8 0,125
1 6 0 , 16 6 ˙
1 5 0,2
1 2 0,5
3 4 0,75

Scientific notation

In science one often needs to work with very large or very small numbers. These can be written more easily in scientific notation, which has the general form

a × 10 m

where a is a decimal number between 0 and 10 that is rounded off to a few decimal places. The m is an integer and if it is positive it represents how many zeros should appear to the right of a . If m is negative, then it represents how many times the decimal place in a should be moved to the left. For example 3 , 2 × 10 3 represents 32 000 and 3 , 2 × 10 - 3 represents 0 , 0032 .

If a number must be converted into scientific notation, we need to work out how many times the number must be multiplied or divided by 10 to make it into anumber between 1 and 10 (i.e. we need to work out the value of the exponent m ) and what this number is (the value of a ). We do this by counting the number of decimal places the decimal point must move.

For example, write the speed of light which is 299 792 458 m · s - 1 in scientific notation, to two decimal places. First, determine where the decimalpoint must go for two decimal places (to find a ) and then count how many places there are after the decimal point to determine m .

Questions & Answers

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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Source:  OpenStax, Siyavula textbooks: grade 10 maths [caps]. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11306/1.4
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