Question

What is 1.83 repeating as a fraction?

Answer 1

1.83838383... = 182/99

1.83333333... = 11/6

1.83183183... = 610/333

Further explanation

Firstly , let us learn about types of sequence in mathematics.

Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.

$T_n = a + (n-1)d$

$S_n = \frac{1}{2}n ( 2a + (n-1)d )$

Tn = n-th term of the sequence

Sn = sum of the first n numbers of the sequence

a = the initial term of the sequence

d = common difference between adjacent numbers

Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.

$T_n = a ~ r^{n-1}$

$S_n = \frac{a( 1 - r^n ) }{1 - r}$

Tn = n-th term of the sequence

Sn = sum of the first n numbers of the sequence

a = the initial term of the sequence

r = common ratio between adjacent numbers

Let us now tackle the problem!

Since the question is not clearly stated, then let me assume the problem is to convert 1.83838383... as a fraction.

Let :

X = 1.8383838383... = 1.83

100X = 183.83838383... = 183.83

100X - X = 183.83 - 1.83

99X = 182

X = 182 ÷ 99

$\large {\boxed {X = \frac{182}{99} } }$

If the problem is to convert 1.833333... as a fraction , then :

Let :

X = 1.833333... = 1.83

10X = 18.33333... = 18.3

100X = 183.3333... = 183.3

100X - 10X = 183.3 - 18.3

90X = 165

X = 165 ÷ 90

$\large {\boxed {X = \frac{11}{6} } }$

If the problem is to convert 1.83183183183... as a fraction , then :

Let :

X = 1.83183183183... = 1.83183

100X = 183.183183... = 183.183

100000X = 183183.183... = 183183.183

100000X - 100X = 183183.183 - 183.183

99900X = 183000

X = 183000 ÷ 99900

$\large {\boxed {X = \frac{610}{333} } }$

Learn more

• Geometric Series : brainly.com/question/4520950
• Arithmetic Progression : brainly.com/question/2966265
• Geometric Sequence : brainly.com/question/2166405

Answer details

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term

Answer 2

The answer to this question would be: 1 5/6

To change a decimal number into fraction, you need to divide the number on the right of decimal point with 1. In this case, the number is 0.83.
This number is hard since .83 doesn't have many factors. To find the answer you can try to multiply the decimal with some number until it close to 1(no decimal left)
0.83* 2= 1.66
0.83* 3= 2.49 ---> close to half, if you find this number, you can try to double it
0.83* 4= 3.32
0.83* 5= 4.15
0.83* 6= 4.98---> close to 1, that means there is high probability that the number can be divided by 6 
0.83 would be 4.98/6, but if we assume that the number is 0.8333...... then 0.83 would be 5/6. So, 1.83 would be 1 5/6