# Squaring Decimal Bases: Products Greater Than 0.1

In numbers such as (0.29)^{2}, the decimal 0.29 is the base and 2 is the exponent. Such numbers are repeated products of the base. Here we are considering exponential numbers where the products are greater than 0.1.

**Rules for Squaring Decimal Bases**

We see that squaring a decimal base is in fact same as multiplying the decimal by itself.

We treat the decimals as whole numbers by ignoring the decimal points and multiply.

After counting the total number of decimal places in these numbers, we put a decimal point after that many places from the right in the answer.

Evaluate (0.33)^{2}

### Solution

**Step 1:**

Consider (0.33)^{2}. We are squaring a decimal base.

**Step 2:**

We treat the decimals as whole numbers by ignoring the decimal points and multiply.

33 × 33 = 1089

**Step 3:**

After counting the total number of decimal places which is four in these numbers, we put a decimal point after four places from the right in the answer.

So, 0.33 × 0.33 = 0.1089

We see that that the product is greater than 0.1

Evaluate (1.01)^{2}

### Solution

**Step 1:**

Consider (1.01)^{2}; here, we are squaring a decimal base.

**Step 2:**

We treat the decimals as whole numbers by ignoring the decimal points and multiply.

101 × 101 = 10201

**Step 3:**

After counting the total number of decimal places which is four in these numbers, we put a decimal point after four places from the right in the answer.

So, 1.01 × 1.01 = 1.0201

We see that that the product is greater than 0.1