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.
Calculating each term Let's calculate each term individually:
1 0 3 = 10 × 10 × 10 = 1000
1 0 1 = 10
1 0 0 = 1 (Any number raised to the power of 0 is 1)
Adding the results Now, let's add the results:
1000 + 10 + 1 = 1011
Final Answer Therefore, the simplified expression is 1011.
Examples
Understanding powers of 10 is crucial in various fields, such as computer science (where binary numbers are based on powers of 2) and finance (where understanding exponential growth is essential for investments). For instance, calculating compound interest involves understanding exponential growth, which is based on powers. If you invest $1000 at an annual interest rate of 5%, the amount you have after 3 years can be calculated using powers: 1000 × ( 1 + 0.05 ) 3 .
