# 5.1 Decimals  (Page 3/8)

 Page 3 / 8

## Write a decimal number from its name.

1. Look for the word “and”—it locates the decimal point.
2. Mark the number of decimal places needed to the right of the decimal point by noting the place value indicated by the last word.
• Place a decimal point under the word “and.” Translate the words before “and” into the whole number and place it to the left of the decimal point.
• If there is no “and,” write a “0” with a decimal point to its right.
3. Translate the words after “and” into the number to the right of the decimal point. Write the number in the spaces—putting the final digit in the last place.
4. Fill in zeros for place holders as needed.

If there is no whole number, we write a 0 to the left of the decimal point as a placeholder. So we would write "nine tenths" as 0.9.

Write twenty-four thousandths as a decimal.

## Solution

 twenty-four thousandths Look for the word "and". There is no "and" so start with 0 0. To the right of the decimal point, put three decimal places for thousandths. Write the number 24 with the 4 in the thousandths place. Put zeros as placeholders in the remaining decimal places. 0.024 So, twenty-four thousandths is written 0.024

Write as a decimal: fifty-eight thousandths.

0.058

Write as a decimal: sixty-seven thousandths.

0.067

Before we move on to our next objective, think about money again. We know that $\text{1}$ is the same as $\text{1.00}.$ The way we write $\text{1}\phantom{\rule{0.2em}{0ex}}\left(\text{or}\phantom{\rule{0.2em}{0ex}}\text{1.00}\right)$ depends on the context. In the same way, integers can be written as decimals with as many zeros as needed to the right of the decimal.

$\begin{array}{cccc}5=5.0\hfill & & & -2=-2.0\hfill \\ 5=5.00\hfill & & & -2=-2.00\hfill \\ 5=5.000\hfill & & & -2=-2.000\hfill \end{array}$
$\text{and so on…}$

## Convert decimals to fractions or mixed numbers

We often need to rewrite decimals as fractions or mixed numbers. Let’s go back to our lunch order to see how we can convert decimal numbers to fractions. We know that $\text{5.03}$ means $5$ dollars and $3$ cents. Since there are $100$ cents in one dollar, $3$ cents means $\frac{3}{100}$ of a dollar, so $0.03=\frac{3}{100}.$

We convert decimals to fractions by identifying the place value of the farthest right digit. In the decimal $0.03,$ the $3$ is in the hundredths place, so $100$ is the denominator of the fraction equivalent to $0.03.$

$0.03=\frac{3}{100}$

For our $\text{5.03}$ lunch, we can write the decimal $5.03$ as a mixed number.

$5.03=5\frac{3}{100}$

Notice that when the number to the left of the decimal is zero, we get a proper fraction. When the number to the left of the decimal is not zero, we get a mixed number.

## Convert a decimal number to a fraction or mixed number.

1. Look at the number to the left of the decimal.
• If it is zero, the decimal converts to a proper fraction.
• If it is not zero, the decimal converts to a mixed number.
• Write the whole number.
2. Determine the place value of the final digit.
3. Write the fraction.
• numerator—the ‘numbers’ to the right of the decimal point
• denominator—the place value corresponding to the final digit
4. Simplify the fraction, if possible.

Write each of the following decimal numbers as a fraction or a mixed number:

$\phantom{\rule{0.2em}{0ex}}4.09$ $\phantom{\rule{0.2em}{0ex}}3.7$ $\phantom{\rule{0.2em}{0ex}}-0.286$

## Solution

 ⓐ 4.09 There is a 4 to the left of the decimal point. Write "4" as the whole number part of the mixed number. Determine the place value of the final digit. Write the fraction. Write 9 in the numerator as it is the number to the right of the decimal point. Write 100 in the denominator as the place value of the final digit, 9, is hundredth. The fraction is in simplest form.

Did you notice that the number of zeros in the denominator is the same as the number of decimal places?

 ⓑ 3.7 There is a 3 to the left of the decimal point. Write "3" as the whole number part of the mixed number. Determine the place value of the final digit. Write the fraction. Write 7 in the numerator as it is the number to the right of the decimal point. Write 10 in the denominator as the place value of the final digit, 7, is tenths. The fraction is in simplest form.

 ⓒ −0.286 There is a 0 to the left of the decimal point. Write a negative sign before the fraction. Determine the place value of the final digit and write it in the denominator. Write the fraction. Write 286 in the numerator as it is the number to the right of the decimal point. Write 1,000 in the denominator as the place value of the final digit, 6, is thousandths. We remove a common factor of 2 to simplify the fraction.

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
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?
what is a peer
What is meant by 'nano scale'?
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
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?