# 5.2 Decimal operations

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

Before you get started, take this readiness quiz.

## Add and subtract decimals

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.

## Add or subtract decimals.

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. $2.51-7.4=-4.89$

#### Questions & Answers

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 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
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?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
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
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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 ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
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
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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