Table of Contents
Number System
Place Value
Number system is a place value system.
Each digit in a number has a place value. Meaning each place is assigned a different value.
Example:
In the number 1234, the 2 is in the hundreds place, the 3 is in the tens place and the 4 is in the ones place.
The number system is based on powers of 10. Because of that each place is progressive power of ten.
| Place | Value | Power |
|---|---|---|
| Billions | 1,000,000,000 | $ 10^9 $ |
| Hundred millions | 100,000,000 | $ 10^8 $ |
| Ten millions | 10,000,000 | $ 10^7 $ |
| Millions | 1,000,000 | $ 10^6 $ |
| Hundred thousands | 100,000 | $ 10^5 $ |
| Ten thousands | 10,000 | $ 10^4 $ |
| Thousands | 1,000 | $ 10^3 $ |
| Hundreds | 100 | $ 10^2 $ |
| Tens | 10 | $ 10^1 $ |
| Ones | 1 | $ 10^0 $ |
Sometimes, numbers are written in expanded notation to show the place value of each digit.
Example:
\begin{align} 843 = 800 + 40 + 3 \\ = (8 \times 100) + (4 \times 10) + (3 \times 1) \\ = (8 \times 10^{2}) + (4 \times 10^{1}) + (3 \times 10^{0}) \\ \end{align}
Round Off Numbers
To round off any number,
Underline the place value to which you are rounding off.
Look to the immediate right (the one to the right). If it is 5 or higher, round your underlined place value up 1 and change all the other numbers to its right to zeros.
If the number is 4 or less, leave your underlined place value as it is and change all the other numbers to its right to zeros.
Round off 724,591 to the nearest ten thousand.
The number 724,591 is rounded down to 720,000.
Repeating Decimals
Commonly used decimals are terminating decimals1)
A repeating decimal is a decimal that continues on indefinetely and repeats a number or block of numbers in a consistent manner.
A vinculum is used to show that a number or block of numbers repeats.
$$ 0.\overline{6} \text{ or } 0.\overline{32} $$