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