Question

Compare and write the appropriate sign $<,>,=$

$2\frac{82}{100}......2.84$

Answer 1

Step 1- Converting $2\frac{82}{100}$ into decimal form.

$2\frac{82}{100}=\frac{100\times 2+82}{100}=\frac{282}{100}$

We know that, to convert a fraction to a decimal, the power of ten in the denominator decides the number of decimal places.

$\frac{282}{100}=\frac{282}{{10}^2}$.

Here, $10$ have a power $2$.

Therefore, we put the decimal after $2$ places from the right side.

So, the decimal form will be $2.82$.

Step 2- Comparing both the numbers.

Now, both the decimals are like decimals as their decimal places are same.

Now, comparing the whole part of the decimals.

Here, the hundredths part of one decimal is $2$ and the second one is $4$.

Therefore, $2.82<2.84$

Hence, $2\frac{82}{100}<2.84$