Is .6 a rational number?

dedica66em
2021-12-16
Answered

Is .6 a rational number?

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servidopolisxv

Answered 2021-12-17
Author has **27** answers

A rational number is a number, which can be described as a ratio of two integers. As it is a ratio of integers, it can be positive as well as negative.

Further, any decimal fraction, which limits itself beyond the decimal point (such as 5.7) which does not go beyond tenth place) or has continuously repeats numbers (till infinity) beyond a certain place of decimal (such as 4.33333... or 0.23124312341325134....) can be easily written as ratio of integers, however large and hence are rational.

Now as$0.6=\frac{6}{10}$ , is a ratio of two integers, it is a rational number.

Further, any decimal fraction, which limits itself beyond the decimal point (such as 5.7) which does not go beyond tenth place) or has continuously repeats numbers (till infinity) beyond a certain place of decimal (such as 4.33333... or 0.23124312341325134....) can be easily written as ratio of integers, however large and hence are rational.

Now as

Anzante2m

Answered 2021-12-18
Author has **34** answers

The basic rule: does it satisfy one of 2 conditions.

Condition 1 Is it a terminating decimal?

Example: 0.125 This stops after the 5 so it terminates

Condition 2 Is it a repeating decimal

Example: 0.356356356356....

written as$0.356\stackrel{\u2015}{356}$

$0.6=\frac{6}{10}$ as this can be written as a fraction it is a rational number.

Condition 1 Is it a terminating decimal?

Example: 0.125 This stops after the 5 so it terminates

Condition 2 Is it a repeating decimal

Example: 0.356356356356....

written as

asked 2021-11-09

Solve algebraically for x

$-\frac{2}{3}(x+12)+\frac{2}{3}x=-\frac{5}{4}x+2$

asked 2022-07-10

How to divide the fraction $1/1+1$

This has to do with re-calculating the sigmoid function in ai. It isn't really important, but the simplest way to put it is I need a math guru to help my monkey brain do this:

$\frac{1}{1+e}$

to like

$\frac{1}{something}+\frac{1}{e}$

Please help me remember my math from high-school if this was ever taught to us.

This has to do with re-calculating the sigmoid function in ai. It isn't really important, but the simplest way to put it is I need a math guru to help my monkey brain do this:

$\frac{1}{1+e}$

to like

$\frac{1}{something}+\frac{1}{e}$

Please help me remember my math from high-school if this was ever taught to us.

asked 2022-06-18

Monotonicity of a fraction.

So I want to prove that the following fraction is monotone increasing, as a part of another proof, that's why I stumbled on:

$\frac{{4}^{n+1}}{2\sqrt{n+1}}\ge \frac{{4}^{n}}{2\sqrt{n}}$

I know it's basic, though how to prove it?

So I want to prove that the following fraction is monotone increasing, as a part of another proof, that's why I stumbled on:

$\frac{{4}^{n+1}}{2\sqrt{n+1}}\ge \frac{{4}^{n}}{2\sqrt{n}}$

I know it's basic, though how to prove it?

asked 2022-07-05

How did he get the fraction with fraction power?

So we have a simple equation that is from Kepler.

${\left(\frac{{\overline{r}}_{1}}{{\overline{r}}_{2}}\right)}^{3}={\left(\frac{{T}_{1}}{{T}_{2}}\right)}^{2}$

In an explanation of a physics book, you can resolve for ${r}_{2}$ like this:

${r}_{2}={r}_{1}{\left(\frac{{T}_{1}}{{T}_{2}}\right)}^{2/3}$

And I found

${r}_{1}=\sqrt[3]{\frac{{T}_{1}^{2}}{{T}_{2}^{2}}{r}_{2}^{3}}$

First question, is my approach correct? My second and main question is how did he get the ${r}_{2}$ equation that I stated first. The physics book doesn't explain how to get from the main equation to ${r}_{2}={r}_{1}{\left(\frac{{T}_{1}}{{T}_{2}}\right)}^{2/3}$. Can someone explain me, please? (By the way, of course the equation for ${r}_{1}$ and ${r}_{2}$ should be different).

Thank you!

So we have a simple equation that is from Kepler.

${\left(\frac{{\overline{r}}_{1}}{{\overline{r}}_{2}}\right)}^{3}={\left(\frac{{T}_{1}}{{T}_{2}}\right)}^{2}$

In an explanation of a physics book, you can resolve for ${r}_{2}$ like this:

${r}_{2}={r}_{1}{\left(\frac{{T}_{1}}{{T}_{2}}\right)}^{2/3}$

And I found

${r}_{1}=\sqrt[3]{\frac{{T}_{1}^{2}}{{T}_{2}^{2}}{r}_{2}^{3}}$

First question, is my approach correct? My second and main question is how did he get the ${r}_{2}$ equation that I stated first. The physics book doesn't explain how to get from the main equation to ${r}_{2}={r}_{1}{\left(\frac{{T}_{1}}{{T}_{2}}\right)}^{2/3}$. Can someone explain me, please? (By the way, of course the equation for ${r}_{1}$ and ${r}_{2}$ should be different).

Thank you!

asked 2021-10-04

write the ratio as a fraction in lowest terms.

$2\frac{3}{4}\text{}\text{to}\text{}1\frac{1}{2}$

$2\frac{3}{4}\text{}\text{is\_\_\_ \% of}\text{}1\frac{1}{2}$

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25% of 4,756,281,5645,215?

asked 2022-05-20

Express the following product as a single fraction:

$(1+\frac{1}{3})(1+\frac{1}{9})(1+\frac{1}{81})\cdots (1+\frac{1}{{3}^{(2n)}})$

I'm having difficulty with this problem:

What i did was:

I rewrote the $1$ as $\frac{3}{3}$

here is what i rewrote the whole product as:

$(\frac{3}{3}+\frac{1}{3})(\frac{3}{3}+\frac{1}{{3}^{2}})(\frac{3}{3}+\frac{1}{{3}^{4}})\cdots (\frac{3}{3}+\frac{1}{{3}^{{2}^{n}}})$

but how would i proceed after this?

$(1+\frac{1}{3})(1+\frac{1}{9})(1+\frac{1}{81})\cdots (1+\frac{1}{{3}^{(2n)}})$

I'm having difficulty with this problem:

What i did was:

I rewrote the $1$ as $\frac{3}{3}$

here is what i rewrote the whole product as:

$(\frac{3}{3}+\frac{1}{3})(\frac{3}{3}+\frac{1}{{3}^{2}})(\frac{3}{3}+\frac{1}{{3}^{4}})\cdots (\frac{3}{3}+\frac{1}{{3}^{{2}^{n}}})$

but how would i proceed after this?