Simplify: [tex]$10^3+10^1+10^0$[/tex]
Answer (1)
Calculate 1 0 3 = 1000 .
Calculate 1 0 1 = 10 .
Calculate 1 0 0 = 1 .
Add the results: 1000 + 10 + 1 = 1011 . The simplified expression is 1011 .
Explanation
Understanding the Problem We are asked to simplify the expression 1 0 3 + 1 0 1 + 1 0 0 . This involves understanding powers of 10 and basic addition.
Calculating Powers of 10 Let's calculate each term individually:
1 0 3 = 10 × 10 × 10 = 1000
1 0 1 = 10
1 0 0 = 1 (Any non-zero number raised to the power of 0 is 1)
Adding the Results Now, we add the results together:
1000 + 10 + 1 = 1011
Final Answer Therefore, the simplified expression is 1011.
Examples
Understanding powers of 10 is crucial in many real-world scenarios, such as calculating large numbers in science, understanding computer memory (kilobytes, megabytes, gigabytes), and dealing with exponential growth or decay in finance and biology. For example, if a bacteria population doubles every hour, understanding exponential growth using powers helps predict the population size after a certain number of hours. Similarly, in finance, compound interest calculations rely heavily on powers to determine the future value of an investment.
