Find the a/b form, where a and b are integers and b isn't equal to 0, for each of the following:
A. 0.29 (29 repeating)
B. 0.00029 (29 repeating)
a/b=.29292929
multiply that by 100
29.292929.
subtract the first from the second
29
so a/b=29/(100-1)=29/99
B.
multipy by 100000
29.292929
subtract then 100 xtimes the original number
29
so a/b=29/(100000-1000)=29/99000
To find the a/b form where a and b are integers (with b not equal to 0) for each of the given decimal numbers, we need to convert them into fractions. Let's solve them one by one:
A. 0.29 (29 repeating):
Let x = 0.292929... (repeating)
Multiply x by 100 to move the decimal point two places to the right:
100x = 29.292929... (repeating)
Subtract x from 100x:
100x - x = 29.292929... - 0.292929... (repeating)
99x = 29
Now, we can see that x = 29/99, which is the a/b form of the given decimal.
Answer: A. 0.29 (29 repeating) can be written as 29/99.
B. 0.00029 (29 repeating):
Let y = 0.000292929... (repeating)
Multiply y by 10000 to move the decimal point four places to the right:
10000y = 29.292929... (repeating)
Subtract y from 10000y:
10000y - y = 29.292929... - 0.000292929... (repeating)
9999y = 29
Now, we can see that y = 29/9999, which is the a/b form of the given decimal.
Answer: B. 0.00029 (29 repeating) can be written as 29/9999.