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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 ms - 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

what is variations in raman spectra for nanomaterials
Jyoti Reply
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
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
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
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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.
Bharti
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
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Siyavula textbooks: grade 10 maths [ncs]. OpenStax CNX. Aug 05, 2011 Download for free at http://cnx.org/content/col11239/1.2
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