Express 3.2304 (dot above 2 and 4) as a fraction
Please show working out too
I don't know which method you use, but here is one of the more common ways ....
let x = 3.230423042304...
multiply by 10000 , (there are 4 digits in the repeating loop, so a zero for each repeating digit)
10000x = 32304.23042304..
subtract them
9999x = 32301
x = 32301/9999 = 3589/1111
shortcut:
look only at the decimal.
for the numerator write down all the digits to the end of the repeating loop --- 2304
subtract all those digits that don't repeat -- none to subtract
for the denominator:
write down a 9 for each of the repeating digits -- 9999
add a zero for each non-repeating digit -- no zeros to add
so 3.230423042304... = 3 + 2304/9999 = 32301/9999 = 3589/1111
given that 6/11= 0.54 write the recurring 0.554 as a fraction 5/33 = 0.15
To express 3.2304 as a fraction, you need to convert the decimal to a fraction.
Step 1: Count the number of decimal places after the whole number. In this case, there are four decimal places.
Step 2: Remove the decimal point and write the number as the numerator of the fraction. In this case, the number is 32304.
Step 3: Write the denominator of the fraction as 1 followed by the same number of zeros as the decimal places. So, the denominator will be 1 followed by four zeros, which is 10,000.
Step 4: Simplify the fraction, if possible. In this case, the fraction 32304/10000 can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 32304 and 10000 is 8, so dividing both numbers by 8 gives 4038/1250.
Therefore, 3.2304 can be expressed as the fraction 4038/1250.