5.7 Simplify and use square roots  (Page 6/8)

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Writing exercises

Why is there no real number equal to $\sqrt{-64}?$

What is the difference between ${9}^{2}$ and $\sqrt{9}?$

Answers will vary. 9 2 reads: “nine squared” and means nine times itself. The expression $\sqrt{9}$ reads: “the square root of nine” which gives us the number such that if it were multiplied by itself would give you the number inside of the square root.

Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter? Why or why not?

Decimals

Name Decimals

In the following exercises, name each decimal.

$0.8$

$0.375$

three hundred seventy-five thousandths

$0.007$

$5.24$

five and twenty-four hundredths

$-12.5632$

$-4.09$

negative four and nine hundredths

Write Decimals

In the following exercises, write as a decimal.

three tenths

nine hundredths

0.09

twenty-seven hundredths

ten and thirty-five thousandths

10.035

negative twenty and three tenths

negative five hundredths

−0.05

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction. Simplify the answer if possible.

$0.43$

$0.825$

$\frac{33}{40}$

$9.7$

$3.64$

$3\frac{16}{25}$

Locate Decimals on the Number Line

Locate the following decimals on a number line.

$\phantom{\rule{0.2em}{0ex}}0.6$

$\phantom{\rule{0.2em}{0ex}}-0.9$

$\phantom{\rule{0.2em}{0ex}}2.2$

$\phantom{\rule{0.2em}{0ex}}-1.3$

Order Decimals

In the following exercises, order each of the following pairs of numbers, using $<$ or $\text{>.}$

$0.6___0.8$

<

$0.2___0.15$

$0.803____0.83$

<

$-0.56____-0.562$

Round Decimals

In the following exercises, round each number to the nearest:

hundredth

tenth

whole number.

$12.529$

1. 12.53
2. 12.5
3. 13

$4.8447$

$5.897$

1. 5.90
2. 5.9
3. 6

Decimal Operations

In the following exercises, add or subtract.

$5.75+8.46$

$32.89-8.22$

24.67

$24-19.31$

$10.2+14.631$

24.831

$-6.4+\left(-2.9\right)$

$1.83-4.2$

−2.37

Multiply Decimals

In the following exercises, multiply.

$\left(0.3\right)\left(0.7\right)$

$\left(-6.4\right)\left(0.25\right)$

−1.6

$\left(-3.35\right)\left(-12.7\right)$

$\left(15.4\right)\left(1000\right)$

15,400

Divide Decimals

In the following exercises, divide.

$0.48÷6$

$4.32÷24$

0.18

$\text{6.29}÷12$

$\left(-0.8\right)÷\left(-0.2\right)$

4

$1.65÷0.15$

$9÷0.045$

200

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Miranda got $\text{40}$ from her ATM. She spent $\text{9.32}$ on lunch and $\text{16.99}$ on a book. How much money did she have left? Round to the nearest cent if necessary.

Jessie put $8$ gallons of gas in her car. One gallon of gas costs $\text{3.528.}$ How much did Jessie owe for all the gas?

$28.22 A pack of $16$ water bottles cost $\text{6.72.}$ How much did each bottle cost? Alice bought a roll of paper towels that cost $\text{2.49.}$ She had a coupon for $\text{0.35}$ off, and the store doubled the coupon. How much did Alice pay for the paper towels?$1.79

Decimals and Fractions

Convert Fractions to Decimals

In the following exercises, convert each fraction to a decimal.

$\frac{3}{5}$

$\frac{7}{8}$

0.875

$-\frac{19}{20}$

$-\frac{21}{4}$

−5.25

$\frac{1}{3}$

$\frac{6}{11}$

$0.\stackrel{\text{—}}{54}$

Order Decimals and Fractions

In the following exercises, order each pair of numbers, using $<$ or $\text{>.}$

$\frac{1}{2}___0.2$

$\frac{3}{5}___0.$

>

$-\frac{7}{8}___-0.84$

$-\frac{5}{12}___-0.42$

>

$0.625___\frac{13}{20}$

$0.33___\frac{5}{16}$

>

In the following exercises, write each set of numbers in order from least to greatest.

$\frac{2}{3},\frac{17}{20},0.65$

$\frac{7}{9},0.75,\frac{11}{15}$

$\frac{11}{15},0.75,\frac{7}{9}$

Simplify Expressions Using the Order of Operations

what is Nano technology ?
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?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
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?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
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
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
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
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
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?
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
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Jeannette has $5 and$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?