# 5.2 Decimal operations

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By the end of this section, you will be able to:
• Multiply decimals
• Divide decimals
• Use decimals in money applications

Before you get started, take this readiness quiz.

Let’s take one more look at the lunch order from the start of Decimals , this time noticing how the numbers were added together.

All three items (sandwich, water, tax) were priced in dollars and cents, so we lined up the dollars under the dollars and the cents under the cents, with the decimal point s lined up between them. Then we just added each column, as if we were adding whole numbers. By lining up decimal s this way, we can add or subtract the corresponding place values just as we did with whole numbers.

1. Write the numbers vertically so the decimal points line up.
2. Use zeros as place holders, as needed.
3. Add or subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.

Add: $3.7+12.4.$

## Solution

 $3.7+12.4$ Write the numbers vertically so the decimal points line up. $\begin{array}{c}\hfill 3.7\\ \hfill \underset{\text{_____}}{+12.4}\end{array}$ Place holders are not needed since both numbers have the same number of decimal places. Add the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers. $\begin{array}{c}\hfill \stackrel{1}{3}.7\\ \hfill \underset{\text{_____}}{+12.4}\\ \hfill 16.1\end{array}$

Add: $5.7+11.9.$

17.6

Add: $18.32+14.79.$

33.11

Add: $23.5+41.38.$

## Solution

 $23.5+41.38$ Write the numbers vertically so the decimal points line up. Place 0 as a place holder after the 5 in 23.5, so that both numbers have two decimal places. Add the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.

Add: $4.8+11.69.$

16.49

Add: $5.123+18.47.$

23.593

How much change would you get if you handed the cashier a $\text{20}$ bill for a $\text{14.65}$ purchase? We will show the steps to calculate this in the next example.

Subtract: $20-14.65.$

## Solution

 $20-14.65$ Write the numbers vertically so the decimal points line up. Remember 20 is a whole number, so place the decimal point after the 0. Place two zeros after the decimal point in 20, as place holders so that both numbers have two decimal places. Subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.

Subtract:

$10-9.58.$

0.42

Subtract:

$50-37.42.$

12.58

Subtract: $2.51-7.4.$

## Solution

If we subtract $7.4$ from $2.51,$ the answer will be negative since $7.4>2.51.$ To subtract easily, we can subtract $2.51$ from $7.4.$ Then we will place the negative sign in the result.

 $2.51-7.4$ Write the numbers vertically so the decimal points line up. Place zero after the 4 in 7.4 as a place holder, so that both numbers have two decimal places. Subtract and place the decimal in the answer. Remember that we are really subtracting $2.51-7.4$ as a place holder, so that both numbers have two decimal places. $2.51-7.4=-4.89$

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
Abigail
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.
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what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
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is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
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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
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
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