Convert eat of the following repeating decimal to a/b form, where a and b are integers and b doesn't equal 0.
a. 0.7
c. 2.37
e. -4.34
0.7777777....=7/9
2.373737373... = 2+37/99=235/99
-4.34343434... = -(4+34/99) = -430/99
To convert the given repeating decimal to the fraction form (a/b), we need to follow these steps:
a. 0.7:
In this case, we have 0.7 which does not have any repeating decimal places. Therefore, it can be directly represented as a fraction.
To convert a decimal to fraction, we need to identify the place value of the digits after the decimal point. In this case, we have one digit after the decimal point, so it is in the tenths place.
Since there is one digit in the tenths place, we can write the decimal 0.7 as 7/10 in fraction form.
So, 0.7 is equal to 7/10.
c. 2.37:
In this case, we have 2.37, where 37 is a repeating decimal part. The repeating decimal part is denoted by a line or a bar above the digits that repeat. In this case, it can be represented as 2.37̅.
To convert 2.37̅ to fraction form, we need to use the following steps:
Step 1: Define the variable x.
Let x = 2.373737... (equation to represent the repeating decimal part)
Step 2: Remove the decimal from the repeating part.
Multiply the variable x by 100 to remove the decimal from the repeating decimal part.
100x = 237.373737...
Step 3: Subtract the original number from the new number to eliminate the repeating part.
Subtract the original variable x from the equation obtained in step 2.
100x - x = 237.373737... - 2.373737...
99x = 235
Step 4: Solve for x.
Divide both sides of the equation by 99.
x = 235/99
Therefore, 2.37̅ can be represented as a fraction, 235/99.
e. -4.34:
In this case, we have a negative repeating decimal. To convert -4.34 to fraction form, we can use similar steps as before.
Step 1: Define the variable x.
Let x = -4.343434... (equation to represent the repeating decimal part)
Step 2: Remove the decimal from the repeating part.
Multiply the variable x by 100 to remove the decimal from the repeating decimal part.
100x = -434.343434...
Step 3: Subtract the original number from the new number to eliminate the repeating part.
Subtract the original variable x from the equation obtained in step 2.
100x - x = -434.343434... - (-4.343434...)
99x = -430
Step 4: Solve for x.
Divide both sides of the equation by 99.
x = -430/99
Therefore, -4.34̅ can be represented as a fraction, -430/99.