Problem 55 - Prealgebra

Question

Population The population of China was 1,355,692,544 in 2014. Round the population to the nearest: a. billion people b. hundred-million people c. million people

Step-by-Step Solution

Answer

a. 1 billionb. 1,400,000,000c. 1,356,000,000

Step 1 - Round to the nearest billion

Review the number provided: 1,355,692,544. Identify the billions place (1 billion). Look at the hundred million place (3). Since 3 is less than 5, do not round up. Thus, 1,355,692,544 rounded to the nearest billion is 1 billion.

Step 2 - Round to the nearest hundred-million

Review the number 1,355,692,544. Identify the hundred-million place (3). Look at the ten million place (5). Since 5 is exactly 5, round up the hundred-million place. Thus, 1,355,692,544 rounded to the nearest hundred-million is 1,400,000,000.

Step 3 - Round to the nearest million

Review the number 1,355,692,544. Identify the million place (5). Look at the hundred thousand place (6). Since 6 is greater than 5, round up the million place. Thus, 1,355,692,544 rounded to the nearest million is 1,356,000,000.

Key Concepts

Place Value

Understanding place value is crucial when working with large numbers. Each digit in a number has a position, and this position holds a specific value. For example, in the number 1,355,692,544:

• The digit '1' is in the billions place.
• The digit '3' is in the hundred-millions place.
• The digit '5' is in the ten-millions place.

Knowing the place value helps you determine how to round numbers correctly.
When rounding, focus on the digit to the immediate right of the place you are rounding to. This helps to decide whether to round up or down.

Population Estimation

Population estimation involves rounding large numbers to make them easier to understand and work with. For example, the population of China in 2014 was 1,355,692,544. Rounding this number helps in quickly conveying information:

• Rounded to the nearest billion: 1 billion
• Rounded to the nearest hundred-million: 1,400,000,000
• Rounded to the nearest million: 1,356,000,000

These estimates simplify communication and make it easier to compare populations across different countries or years. Estimation is particularly useful in daily contexts and when making rough comparisons.

Rounding Rules

Rounding rules are straightforward once you grasp the key idea. Here’s a step-by-step guide to help you:
1. Identify the digit in the place you are rounding to.
2. Look one digit to the right:

• If that digit is 5 or more, round the target digit up by one.
• If that digit is less than 5, keep the target digit the same.

Using the exercise as an example, if you need to round 1,355,692,544 to the nearest hundred-million:
1. The digit in the hundred-millions place is '3'.
2. Look at the digit to the right ('5' in the ten-millions place).
3. Since '5' is equal to 5, round up to get 1,400,000,000.
Following these simple rules helps ensure accurate rounding every time.