What is the expanded form of 23.75 using base-10 number notation?
The expanded form of 23.75 using base-10 number notation is:
(2 * 10^1) + (3 * 10^0) + (7 * 10^-1) + (5 * 10^-2)
To find the expanded form of the number 23.75 using base-10 number notation, we can break down the number into its individual place values:
In base-10 number notation, each digit in a number represents a different place value, ranging from right to left as follows:
- Units: 1
- Tens: 10
- Hundreds: 100
- Thousands: 1,000
- Ten thousands: 10,000
- Hundred thousands: 100,000
- Millions: 1,000,000
Now let's explore the place values of 23.75:
- 20 is in the tens place (20 * 10)
- 3 is in the units place (3 * 1)
- 0.7 is in the tenths place (0.7 * 0.1)
- 0.05 is in the hundredths place (0.05 * 0.01)
So the expanded form of 23.75 using base-10 number notation is:
20 * 10 + 3 * 1 + 0.7 * 0.1 + 0.05 * 0.01
Simplified, this is equal to:
200 + 3 + 0.07 + 0.0005