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shtirl [24]
4 years ago
11

X = 0.045 Prove algebraically that x can be written as 1/22

Mathematics
2 answers:
kenny6666 [7]4 years ago
8 0

Answer:

Lets suppose this number is recurring, then we can prove.

x=0.045 (45 is recurring)

10x=0.45 (45 is recurring)

=> 100x =4.54 (54 is recurring)

=> 1000x= 45.45 (45 is recurring)

We will subtract 1000x-10x to get rid of the decimals:

1000x-10x = 45.45-0.45

990x =45

=> x =45/990

Dividing by 5

=>x= 9/198

Now dividing by 9

x =1/22

Hence, proved.

blagie [28]4 years ago
7 0
The least decimal place in 0.045 is found in the thousandths place. Thus, if expressed as a fraction, it would be 45/1000. Let's substitute this to the equation:

x = 45/1000
1000x = 45
(1000/45)x = 1
 
When you divide 1000 by 45, the quotient would be 22.2222222... This could be round to the nearest whole number which is 22. Then,

22x = 1
x = 1/22

I hope I was able to answer your question. Have a good day.
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