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Write as a fraction or mixed number. Simplify the answer if possible.

5.3 6.07 −0.234

  1. 5 3 10
  2. 6 7 100
  3. 234 1000

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Write as a fraction or mixed number. Simplify the answer if possible.

8.7 1.03 −0.024

  1. 8 7 10
  2. 1 3 100
  3. 24 1000

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Locate decimals on the number line

Since decimals are forms of fractions, locating decimals on the number line is similar to locating fractions on the number line.

Locate 0.4 on a number line.

Solution

The decimal 0.4 is equivalent to 4 10 , so 0.4 is located between 0 and 1 . On a number line, divide the interval between 0 and 1 into 10 equal parts and place marks to separate the parts.

Label the marks 0.1 , 0.2 , 0.3 , 0.4 , 0.5 , 0.6 , 0.7 , 0.8 , 0.9 , 1.0 . We write 0 as 0.0 and 1 as 1.0 , so that the numbers are consistently in tenths. Finally, mark 0.4 on the number line.
A number line is shown with 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 labeled. There is a red dot at 0.4.

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Locate 0.6 on a number line.


This image shows a number line from 0.0 to 1.0 and segmented into tenths.  A point is plotted at 0.6 on the number line.

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Locate 0.9 on a number line.


This image shows a number line from 0.0 to 1.0 and segmented into tenths.  A point is plotted at 0.9 on the number line.

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Locate −0.74 on a number line.

Solution

The decimal −0.74 is equivalent to 74 100 , so it is located between 0 and −1 . On a number line, mark off and label the hundredths in the interval between 0 and −1 ( −0.10 , −0.20 , etc.) and mark −0.74 between −0.70 and −0.80, a little closer to −0.70 .
A number line is shown with negative 1.00, negative 0.90, negative 0.80, negative 0.70, negative 0.60, negative 0.50, negative 0.40, negative 0.30, negative 0.20, negative 0.10, and 0.00 labeled. There is a red dot between negative 0.80 and negative 0.70 labeled as negative 0.74.

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Locate −0.63 on a number line.


This image shows a number line from -1.00 to 0.00 . A point is plotted at negative 0.63 on the number line.

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Locate −0.25 on a number line.


This image shows a number line from -1.00 to 0.00 . A point is plotted at negative 0.25 on the number line.

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Order decimals

Which is larger, 0.04 or 0.40 ?

If you think of this as money, you know that $0.40 (forty cents) is greater than $0.04 (four cents). So,

0.40 > 0.04

In previous chapters, we used the number line to order numbers.

a < b a is less than b when a is to the left of b on the number line a > b a is greater than b when a is to the right of b on the number line

Where are 0.04 and 0.40 located on the number line?

A number line is shown with 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 labeled. There is a red dot between 0.0 and 0.1 labeled as 0.04. There is another red dot at 0.4.

We see that 0.40 is to the right of 0.04 . So we know 0.40 > 0.04 .

How does 0.31 compare to 0.308 ? This doesn’t translate into money to make the comparison easy. But if we convert 0.31 and 0.308 to fractions, we can tell which is larger.

0.31 0.308
Convert to fractions. 31 100 308 1000
We need a common denominator to compare them. . 308 1000
310 1000 308 1000

Because 310 > 308 , we know that 310 1000 > 308 1000 . Therefore, 0.31 > 0.308 .

Notice what we did in converting 0.31 to a fraction—we started with the fraction 31 100 and ended with the equivalent fraction 310 1000 . Converting 310 1000 back to a decimal gives 0.310 . So 0.31 is equivalent to 0.310 . Writing zeros at the end of a decimal does not change its value.

31 100 = 310 1000 and 0.31 = 0.310

If two decimals have the same value, they are said to be equivalent decimals.

0.31 = 0.310

We say 0.31 and 0.310 are equivalent decimals.

Equivalent decimals

Two decimals are equivalent decimals    if they convert to equivalent fractions.

Remember, writing zeros at the end of a decimal does not change its value.

Order decimals.

  1. Check to see if both numbers have the same number of decimal places. If not, write zeros at the end of the one with fewer digits to make them match.
  2. Compare the numbers to the right of the decimal point as if they were whole numbers.
  3. Order the numbers using the appropriate inequality sign.

Order the following decimals using < or >:

0.64 __ 0.6

0.83 __ 0.803

Solution

0.64 __ 0.6
Check to see if both numbers have the same number of decimal places. They do not, so write one zero at the right of 0.6. 0.64 __ 0.60
Compare the numbers to the right of the decimal point as if they were whole numbers. 64 > 60
Order the numbers using the appropriate inequality sign. 0.64 > 0.60

0.64 > 0.6
0.83 __ 0.803
Check to see if both numbers have the same number of decimal places. They do not, so write one zero at the right of 0.83. 0.830 __ 0.803
Compare the numbers to the right of the decimal point as if they were whole numbers. 830 > 803
Order the numbers using the appropriate inequality sign. 0.830 > 0.803

0.83 > 0.803
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Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
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what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
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algebra 2 Inequalities:If equation 2 = 0 it is an open set?
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or infinite solutions?
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The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
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Kristine 2*2*2=8
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No. 7x -4y is simplified from 4x + (3y + 3x) -7y
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J, combine like terms 7x-4y
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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preparation of nanomaterial
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
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what is system testing
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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
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anybody can imagine what will be happen after 100 years from now in nano tech world
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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
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name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
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silver nanoparticles could handle the job?
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not now but maybe in future only AgNP maybe any other nanomaterials
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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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the Beer law works very well for dilute solutions but fails for very high concentrations. why?
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how do you translate this in Algebraic Expressions
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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Practice Key Terms 1

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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