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3 years ago

What is 0.(24) ̅ (the 24 is repeating) expressed as a fraction in simplest form?

1 answer:

7 0

Hi,
a)let 0.24 be x.
100x(two zeros because two decimals are repeating)=24.24 ̅(24 is repeating)
Now subtract 100x-x on both sides. This forms an equation.
100x-x=24.24(.24 is repeating) -0.24(.24 is repeating)
99x=24
x=24/99
simplest form=8/33
b)Follow the same rule.
let 0.24(4 is repeating) be x
Since there is two decimals in total , 100x=24.44(4 is repeating)
But since there is one decimal that is repeating, there will be one zero. Hence it will become 100x-10x= 24.4(4 is repeating)-2.4(4 is repeating and get the decimal point closest to the repeating decimal)
90x=22
x=22/90
Simplest form=11/45
c) 0.24 is expressed as 8/25
0.24/1
24/100(make it a whole number and add no. of zeros based on how many decimals places you move.)
Simplest form=6/25
Hope this helps you.

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stellarik [79]

Step 1:

first let us convert the two decimals into fractions.

0.36=36/100 (since there are two digits after decimal point we divide by 100)

2.4=24/10 (since there are one digit after decimal point we divide by 10)

now we can multiply the fractions

$\frac{36}{100}$ × $\frac{24}{10}$

multiplying numerator with numerator and denominator with denominator:

$\frac{36*24}{100*10}$

= $\frac{864}{1000}$

Now we can convert this back to decimal

864/1000=0.864, moving decimal three digits to the left since we have three zeros in the denominator that is 1000.

Answer=0.864

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If r and s are positive integers, is \small \frac{r}{s} an integer? (1) Every factor of s is also a factor of r. (2) Every prime

Yuri [45]

Answer:

If statement(1) holds true, it is correct that $\small \frac{r}{s}$ is an integer.

If statement(2) holds true, it is not necessarily correct that $\small \frac{r}{s}$ is an integer.

Step-by-step explanation:

Given two positive integers $r$ and $s$ .

To check whether $\small \frac{r}{s}$ is an integer:

Condition (1):

Every factor of $s$ is also a factor of $r$ .

$r \geq s$

Let us consider an example:

$s = 5^2 \cdot 2\\r = 5^3 \cdot 2^2$

$\dfrac{r}{s} = \dfrac{5^3\cdot2^2}{5^2\cdot2} = 10$

which is an integer.

Actually, in this situation $s$ is a factor of $r$ .

Condition 2:

Every prime factor of s is also a prime factor of r.

(But the powers of prime factors need not be equal as we are not given the conditions related to powers of prime factors.)

Let

$r = 2^2\cdot 5\\s =2^4\cdot 5$

$\dfrac{r}{s} = \dfrac{2^3\cdot5}{2^4\cdot5} = \dfrac{1}{2}$

which is not an integer.

So, the answer is:

If statement(1) holds true, it is correct that $\small \frac{r}{s}$ is an integer.

If statement(2) holds true, it is not necessarily correct that $\small \frac{r}{s}$ is an integer.

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The original amount of peas that Julia had at first was 120.

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3 years ago

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