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Chapter 1: Problem 18

The table below shows the populations of four countries in 2016. Write expanded notation for the given population. $$ 1,266,883,598 \text { for India } $$

Short Answer

Expert verified
1,000,000,000 + 200,000,000 + 60,000,000 + 6,000,000 + 800,000 + 80,000 + 3,000 + 500 + 90 + 8

Step by step solution

01

Understand the Number

The given population for India is 1,266,883,598. Expanded notation breaks this number down based on the place values of its digits.
02

Identify Place Values

Identify the place value of each digit in 1,266,883,598 from left to right: 1 is in the billions place, 2 is in the hundred millions place, 6 is in the ten millions place, 6 is in the millions place, 8 is in the hundred thousands place, 8 is in the ten thousands place, 3 is in the thousands place, 5 is in the hundreds place, 9 is in the tens place, 8 is in the ones place.
03

Write Each Digit with its Place Value

Write each digit with its place value to form the expanded notation. 1,000,000,000 + 200,000,000 + 60,000,000 + 6,000,000 + 800,000 + 80,000 + 3,000 + 500 + 90 + 8.

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Key Concepts

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

place value
Place value is a fundamental concept in mathematics, helping us understand the value of numbers based on their position. In any number, each digit has a place value, determined by its position. For instance, in the number 1,266,883,598, the leftmost digit '1' has the place value of one billion.
Understanding place value is crucial. By knowing the place value, students can read, write, and interpret large numbers correctly.
  • The place value from right to left is: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, hundred millions, billions.
  • Example: In 1,266,883,598, the '9' is in the tens place, making it worth 90.
Place value ensures we can break down and simplify large numbers for better comprehension.
large numbers
Dealing with large numbers can often be overwhelming. However, expanding these numbers using place value can simplify them. For example, the population of India in 2016, given as 1,266,883,598, may seem intimidating at first glance.
  • By breaking it down, it forms into smaller, manageable parts like 1 billion, 200 million, 60 million, etc.
  • This helps to comprehend large numerical data, making it easier to work with.
Understanding large numbers using an expanded notation method allows interpreting and analyzing data like population statistics effortlessly.
mathematical notation
Mathematical notation is a way of writing numbers and symbols to represent concepts. Expanded notation is one such form, where a number is shown as the sum of each digit multiplied by its place value. This helps in visualizing and understanding the number better.
  • Example for India鈥檚 population: 1,266,883,598 can be written as: \[1 \times 10^9 + 2 \times 10^8 + 6 \times 10^7 + 6 \times 10^6 + 8 \times 10^5 + 8 \times 10^4 + 3 \times 10^3 + 5 \times 10^2 + 9 \times 10^1 + 8 \times 10^0\]
Using expanded notation shows the value and importance of each digit in a large number, ensuring there is no loss of significant information.
population data
Population data is often presented in large numbers, which can be daunting. For example, India's population in 2016 was 1,266,883,598. Understanding such data necessitates breaking down these figures using the place value system and expanded notation.
  • This breakdown helps understand the magnitude as well as the structure of the number.
  • From billions to ones, each place value carried a part of the population count.
Learning to interpret population data correctly is essential for subjects like geography and social studies, where analysis of such data is integral.

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