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Chapter 1: Problem 43

Solve each percent problem. In \(2013,\) mobile messaging service WhatsApp had 300 million monthly active users worldwide. By \(2017,\) this number had increased \(333.3 \% .\) To the nearest million, what was the number of WhatsApp monthly active users worldwide in \(2017 ?\)

Short Answer

Expert verified
1,300 million

Step by step solution

01

Identify the Initial Value

The initial number of WhatsApp monthly active users in 2013 is given as 300 million.
02

Understand the Percentage Increase

The problem states that the number of users increased by 333.3%. This means we need to add 333.3% of the initial value to the initial value.
03

Convert Percentage to Decimal

Convert 333.3% to a decimal by dividing by 100: \[333.3 \div 100 = 3.333\]
04

Calculate the Increase

Multiply the initial value by the decimal to find the increase: \[300 \times 3.333 = 999.9\]
05

Find the Total Number of Users

Add the increase to the initial value to get the number of users in 2017: \[300 + 999.9 = 1,299.9\]
06

Round to the Nearest Million

The problem asks for the number of users rounded to the nearest million. So, \[1,299.9\] rounds to \[1,300\] million.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

initial value identification
To start solving a percentage increase problem, identify the initial value. In this example, we are given the number of WhatsApp monthly active users in 2013, which is 300 million. This initial value is the baseline amount before any increase is applied.
Identifying this initial value is crucial because it sets the stage for all the following calculations. Every further step revolves around this number.
percentage to decimal conversion
To work with percentages in mathematical calculations, we need to convert them to decimal form. This conversion allows us to perform operations like multiplication.
A percentage can be converted to a decimal by dividing by 100. For example, in our problem, we have a 333.3% increase. To convert 333.3% to a decimal, we perform the following calculation:
\[ 333.3 \div 100 = 3.333 \]
Now we have 3.333 as the decimal representation of 333.3%. This decimal can now be used in our calculations.
multiplication of percentages
Once we've converted our percentage to a decimal, the next step is to multiply that decimal by the initial value. This gives us the total increase amount.
Here, we need to calculate 333.3% of 300 million. Using our decimal conversion, we multiply: \[ 300 \times 3.333 = 999.9 \]
This tells us that the 300 million users increased by 999.9 million users.
rounding numbers
Finally, once you have the total number of users, you may need to round the number to make it more presentable, as often required by the problem.
In our exercise, the total number of WhatsApp users in 2017 was calculated as: \[ 300 + 999.9 = 1,299.9 \] million.
To round this number to the nearest million, we look at the first decimal place. Since 299.9 rounds to 300, we get: \[ 1,299.9 \approx 1,300 \] million.
So the approximated number of WhatsApp monthly active users worldwide in 2017 is 1,300 million.

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