Question

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

$5\frac{1}{4}.............5.25$

Answer 1

Step 1- Converting $5\frac{1}{4}$ into decimal form.

$5\frac{1}{4}=\frac{5\times 4+1}{4}=\frac{21}{4}$.

Changing the denominator in the multiple of $10$.

$\frac{21}{4}=\frac{21\times 25}{4\times 25}=\frac{525}{100}$

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

$\frac{525}{100}=\frac{525}{{10}^2}$.

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

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

So, the decimal form will be $5.25$.

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.

$5.25=5.25$

Hence, $5\frac{1}{4}=5.25$