Final answer:
The expanded form of the number 20 + 5 + 0.100 + 0.3 + 0.8 is 2 × 10 + 5 × 1 + 1 × 0.1 + 3 × 0.1 + 8 × 0.1. It represents the sum of each digit's value in the number, considering its place value. Significant figures and scientific notation may alter how zeros and place values are represented.
Step-by-step explanation:
To write the expanded form of the number 20 + 5 + 0.100 + 0.3 + 0.8, we should consider the value of each digit in the number. Expanded form is a way of writing numbers to show the value of each digit. It is especially useful for understanding the place value of digits in larger numbers. Let's break down each component of this number to fully understand it.
The digits '20' represent twenty, which can be written as 2 × 10. The digit '5' is just five or 5 × 1. When we look at decimals like '0.100', '0.3', and '0.8', we see that these need to be expressed in relation to their decimal place value. For example, '0.100' is the same as a hundredth, which can be written as 1 × 0.1. The '0.3' is three tenths, which is the same as 3 × 0.1. Lastly, '0.8' is eight tenths, or 8 × 0.1.
Combining these values gives us the expanded form: 2 × 10 + 5 × 1 + 1 × 0.1 + 3 × 0.1 + 8 × 0.1. We simply added the multiples of each place value together to get the expanded form of the number.
It's important to note that when expressing numbers in scientific notation or as a series of significant figures, the structure changes somewhat. For instance, using scientific notation, the zeroes preceding significant figures (like in '0.100') are not considered significant and we would use an exponent to indicate the position of the decimal point. A number like 965 would be expressed in scientific notation as 9.65 × 10², meaning the decimal point has been moved two places to the left.