quotients, decimals and intergers Help

[carlycup]

Havent done Math in a while. Help. Know the definitions of terms, intergers, quotients and decimals, but need help.
How do you do the following?


Show that each decimal can be written as a quotient of two intergers? ex. 3.375
I have a list to do and think I can probably figure them out, just need to know how to get started?

 

[mmm4444bot]

Do you understand that the part to the right of the decimal point means 375 thousandths?

In other words, the decimal number 3.375 represents the sum 3 + 375/1000.

All that you need to do is combine this into a single fraction.

If you've forgotten how to add fractions, or you've forgotten the meaning of decimal numbers (i.e., the tenths place, hundredths place, thousandths place, et cetera), then let us know and we can post links to some lessons for you.

Cheers :cool:

 

[mmm4444bot]

Two more thoughts, for you.

The correct spelling is "Integer" (IN-tah-juhr).

I know a lot of people define Rational numbers as Real numbers that may be expressed as a ratio of Integers, but I prefer to frame the definition as a ratio of an Integer to a Natural number.

This definition avoids division by zero.

 

[carlycup]

Do you understand that the part to the right of the decimal point means 375 thousandths?

In other words, the decimal number 3.375 represents the sum 3 + 375/1000.

All that you need to do is combine this into a single fraction.

If you've forgotten how to add fractions, or you've forgotten the meaning of decimal numbers (i.e., the tenths place, hundredths place, thousandths place, et cetera), then let us know and we can post links to some lessons for you.

Cheers :cool:

Yes, Understand 3 + 375/1000. Thanks\

But when problem says "Show that each decimal can be written as a quotient of two integers. Ex. 3.375 ; Ex. .18 ; etc. Dont' know how to do that.
Thanks for all the help you can give to get me on my way.

 

[mmm4444bot]

But when problem says "Show that each decimal can be written as a quotient of two integers["]

Don't know how to do that.

Gosh, did you try what I suggested?

Just to be sure, please confirm that you also understand the meaning of the phrase "quotient of two integers".

A quotient of two Integers is simply a ratio (i.e., a fraction) where the numerator is an Integer and the denominator is an Integer (other than zero, of course).

What do you get after adding 3 + 375/1000 ?

Show me, and, based on what I see, I may explain for you a shortcut. :cool:

 

[JeffM]

Yes, Understand 3 + 375/1000. Thanks\

But when problem says "Show that each decimal can be written as a quotient of two integers. Ex. 3.375 ; Ex. .18 ; etc. Dont' know how to do that.
Thanks for all the help you can give to get me on my way.

A rational number can be expressed in many ways, ONE of which is in decimal form.

The normal definition of a rational number is that it is one integer divided by another integer (other than zero).

Example $\displaystyle 0.5 = \dfrac{1}{2} = \dfrac{2}{4} = \dfrac{3}{6} = \dfrac{4}{8} = \dfrac{5}{10}....$

These are all different ways to express the same rational number.

So every number represented in decimal form can be expressed in terms of a fraction, the denominator of which is a power of 10, and the numerator of which is your original number without a decimal point.

Do you know what a power of 10 is?

$\displaystyle 10^0 = 1\ and\ n \ge 1 \implies 10^n = 10 * 10^{n - 1}.$

$\displaystyle So\ 10^0 = 1,\ 10^1 = 10 * 1 = 10,\ 10^2 = 10 * 10 = 100,\ 10^3 = 10 * 100 = 1,000\ etc.$

The powers of 10 are easy to remember because the nth power of 10 is just 1 followed by n zeroes.

If you count the number of digits to the right of the decimal point, that is the power of 10 to use. In 3.375 there are 3 digits to the right of the decimal so you want the denominator to be 10 to the third power = 1000 (1 followed by three zeroes). And the numerator is the number without a decimal point.

$\displaystyle 3.375 = \dfrac{3,375}{1,000}.$

 

[pka]

Havent done Math in a while. Help. Know the definitions of terms, intergers, quotients and decimals, but need help. How do you do the following?

Show that each decimal can be written as a quotient of two of two intergers

But of course that is not true. Unless you mean that if a number has a closed form of a decimal.
Think about $\displaystyle \dfrac{\pi}{3}$.

 

[carlycup]

Gosh, did you try what I suggested?

Just to be sure, please confirm that you also understand the meaning of the phrase "quotient of two integers".

A quotient of two Integers is simply a ratio (i.e., a fraction) where the numerator is an Integer and the denominator is an Integer (other than zero, of course).

What do you get after adding 3 + 375/1000 ?

Show me, and, based on what I see, I may explain for you a shortcut. :cool:

Thank you, sorry, I was just making it harder than it is. I understand. Like I said, its been awhile. Again, Thanks

 

[mmm4444bot]

But of course that is not true.

Not in general, but the exercise's list of numbers likely contains only terminating decimals.

If it contains any repeating decimals, I expect the student to return.

 

[Deleted member 4993]

Not in general, but the exercise's list of numbers likely contains only terminating decimals.

If it contains any repeating decimals, I expect the student to return.

Actually, irrational numbers are infinite-non-repeating decimals.

The infinite-repeating decimals can be expressed as ratio of integers via several tricks in arithmetic.

 

[mmm4444bot]

I understand.

Thanks

You're welcome. Don't forget to reduce all ratios to lowest terms.

3.375 = 27/8

:cool: