Question

Find each result without using a grid. \(65 \%\) of 210

Short answer

136.5

Step-by-step solution

- Convert Percentage to Decimal

First, convert the percentage into a decimal. To do this, divide the percentage by 100. \(65\% = \frac{65}{100} = 0.65\)

- Multiply the Decimal by the Number

Next, multiply the decimal by the given number to find the result.\(0.65 \times 210\)

- Perform the Multiplication

Carry out the multiplication by computing:\(0.65 \times 210 = 136.5\)

Key concepts

converting percentages to decimals

Understanding percentages is crucial in mathematics. A percentage represents a fraction of 100. Convert percentages to decimals by dividing by 100. For example, converting 65% involves dividing 65 by 100. Mathematically, this is shown as:

• 65 ÷ 100

Which equals 0.65. Essentially, you're moving the decimal point two places to the left. This conversion helps simplify calculations.

multiplication of decimals

Decimal multiplication may seem tricky, but it is straightforward with practice. To multiply decimals, forget the decimal points initially. Just multiply as if they are whole numbers. For example, multiplying 0.65 by 210, think of 65 and 210 first.
Now, perform the multiplication:

• 65 × 210 = 13650

Next, count the number of decimal places in the original numbers. Here, 0.65 has two decimal places. So, place the decimal point accordingly in the product:

• 13650 becomes 136.50

Therefore, 0.65 × 210 = 136.5.

step-by-step problem solving

Breaking problems into smaller steps can make them easier to handle. Let's apply this to our example problem:

• Step 1: Convert 65% to a decimal by dividing by 100, yielding 0.65.


• Step 2: Multiply the decimal by the given number: 0.65 × 210.


• Step 3: Perform the multiplication. First, calculate as if they are whole numbers: 65 × 210 = 13650. Then, adjust the decimal point: 13650 becomes 136.5 since 0.65 has two decimal places.

This structured approach ensures you don't miss any important steps. It also makes complex problems more manageable.