Final answer:
To prove 0.136×0.2 equals 1/33, we multiply 0.136 by 0.2, convert the result into a fraction, and then simplify it. Upon simplifying, we find that it is equal to 1/33.
Step-by-step explanation:
To prove that 0.136×0.2 is equal in value to 1/33, we can start by multiplying 0.136 by 0.2:
0.136×0.2 = 0.0272. We then need to express 0.0272 as a fraction to compare it to 1/33.
Notice that 0.0272 can be written as 272/10000, which simplifies to 34/1250. Further simplifying this fraction, we divide both the numerator and denominator by 34, which results in 1/36.7. To make the comparison easier, we can convert 1/33 into a decimal:
1/33 ≈ 0.030303 repeating. However, we know that 1/33 is a fixed value and not an approximation, so let's manipulate the fraction 1/36.7 to get an exact match. Multiplying numerator and denominator by 3 gives us 3/110.1. Here, we can see that if we multiply by another 3, we get 9/330.3, and multiplying by 3 once more provides us 27/990.9.
Finally, multiplying both the numerator and the denominator by 11 (which is 33×0.3), we get 297/10899, and upon further inspection, this fraction simplifies to 1/33, proving the original statement.