Finding a percentage of a whole number without a calculator: Advanced

Introduction

We can find the percentages of whole numbers without a calculator in some cases where standard percentages are involved. Some standard percentages are like 1%, 10%, 25%, 50%, 100%. Other percentages can be written as combinations of these standard percentages. Like 2% is twice of 1%; 5% is half of 10%, 20% is twice of 10% and so on.

Rules to find the percentage of a whole number without a calculator

To find 1% of any whole number, we shift the decimal two places to the left in the whole number.
To find 10% of any whole number, we shift the decimal one place to the left in the whole number.
To find 25% of any whole number, we divide the whole number by 4.
To find 50% of any whole number, we divide the whole number by 2.
To find 100% of any whole number, we keep the whole number as it is.
To find other percentages of whole numbers, we use the combinations of the standard percentages to find them.

Example 1:

What is 2% of 19.5?

Solution

Step 1:

To find 1% of any whole number, we shift the decimal two places to the left in the whole number. To find 2% of any whole number, we double the 1% of that number.

Step 2:

1% of 19.5 is found by shifting the decimal point two places to left

1% of 19.5 = 0.195

So, 2% of 19.5 = 2 × 1% of 19.5 = 2 × 0.195 = 0.390 = 0.39

Example 2:

What is 30% of 7.25?

Solution

Step 1:

To find 10% of any whole number, we shift the decimal one place to the left in the whole number. To find 30% of any whole number, we triple the 10% of that number.

Step 2:

10% of 7.25 is found by shifting the decimal point one place to left

10% of 7.25 = 0.725

So, 30% of 7.25 = 3 × 10% of 7.25 = 3 × 0.725 = 2.175

Example 3:

What is 15% of 40?

Solution

Step 1:

15% can be written as a sum of 10% and 5%

To find 10% of any whole number, we shift the decimal one place to the left in the whole number. To find 5% of any whole number, we divide the 10% of that number by 2.

Step 2:

10% of 40 is found by shifting the decimal point one place to left

10% of 40.0 = 4.00; 5% of 40 = $\frac{(10\%\:of \:40.0)}{2} = \frac{4}{2} = 2$

15% of 40 = 10% of 40 + 5% of 40 = 4 + 2 = 6

So, 15% of 40 = 6