# 6.1 Reading and writing decimals

 Page 1 / 2
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to read and write decimals. By the end of the module students should understand the meaning of digits occurring to the right of the ones position, be familiar with the meaning of decimal fractions and be able to read and write a decimal fraction.

## Section overview

• Digits to the Right of the Ones Position
• Decimal Fractions
• Reading Decimal Fractions
• Writing Decimal Fractions

## Digits to the right of the ones position

We began our study of arithmetic ( [link] ) by noting that our number system is called a positional number system with base ten. We also noted that each position has a particular value. We observed that each position has ten times the value of the position to its right.

This means that each position has $\frac{1}{10}$ the value of the position to its left.

Thus, a digit written to the right of the units position must have a value of $\frac{1}{\text{10}}$ of 1. Recalling that the word "of" translates to multiplication $\left(\cdot \right)$ , we can see that the value of the first position to the right of the units digit is $\frac{1}{\text{10}}$ of 1, or

$\frac{1}{\text{10}}\cdot 1=\frac{1}{\text{10}}$

The value of the second position to the right of the units digit is $\frac{1}{\text{10}}$ of $\frac{1}{\text{10}}$ , or

$\frac{1}{\text{10}}\cdot \frac{1}{\text{10}}=\frac{1}{{\text{10}}^{2}}=\frac{1}{\text{100}}$

The value of the third position to the right of the units digit is $\frac{1}{\text{10}}$ of $\frac{1}{\text{100}}$ , or

$\frac{1}{\text{10}}\cdot \frac{1}{\text{100}}=\frac{1}{{\text{10}}^{3}}=\frac{1}{\text{1000}}$

This pattern continues.

We can now see that if we were to write digits in positions to the right of the units positions, those positions have values that are fractions. Not only do the positions have fractional values, but the fractional values are all powers of 10 $\left(\text{10},{\text{10}}^{2},{\text{10}}^{3},\dots \right)$ .

## Decimal point, decimal

If we are to write numbers with digits appearing to the right of the units digit, we must have a way of denoting where the whole number part ends and the fractional part begins. Mathematicians denote the separation point of the units digit and the tenths digit by writing a decimal point . The word decimal comes from the Latin prefix "deci" which means ten, and we use it because we use a base ten number system. Numbers written in this form are called decimal fractions , or more simply, decimals .

Notice that decimal numbers have the suffix "th."

## Decimal fraction

A decimal fraction is a fraction in which the denominator is a power of 10.

The following numbers are examples of decimals.

1. 42.6

The 6 is in the tenths position.

$\text{42}\text{.}6=\text{42}\frac{6}{\text{10}}$

2. 9.8014

The 8 is in the tenths position.
The 0 is in the hundredths position.
The 1 is in the thousandths position.
The 4 is in the ten thousandths position.

$9\text{.}\text{8014}=9\frac{\text{8014}}{\text{10},\text{000}}$

3. 0.93

The 9 is in the tenths position.
The 3 is in the hundredths position.

$0\text{.}\text{93}=\frac{\text{93}}{\text{100}}$

Quite often a zero is inserted in front of a decimal point (in the units position) of a decimal fraction that has a value less than one. This zero helps keep us from overlooking the decimal point.
4. 0.7

The 7 is in the tenths position.

$0\text{.}7=\frac{7}{\text{10}}$

We can insert zeros to the right of the right-most digit in a decimal fraction without changing the value of the number.
$\frac{7}{\text{10}}=0\text{.}7=0\text{.}\text{70}=\frac{\text{70}}{\text{100}}=\frac{7}{\text{10}}$

## Reading a decimal fraction

To read a decimal fraction,
1. Read the whole number part as usual. (If the whole number is less than 1, omit steps 1 and 2.)
2. Read the decimal point as the word "and."
3. Read the number to the right of the decimal point as if it were a whole number.
4. Say the name of the position of the last digit.

#### Questions & Answers

what does nano mean?
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?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
how to synthesize TiO2 nanoparticles by chemical methods
Zubear
what's the program
Jordan
?
Jordan
what chemical
Jordan
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
7hours 36 min - 4hours 50 min