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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 can chip be made from sand
Eke Reply
is this allso about nanoscale material
Almas
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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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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