Place value and number systems

Place value

Our number system uses ten digits, $0$ to $9$. The position of a digit tells you its value. Each place is worth ten times the place to its right.

Expanded form writes a number as the sum of its place values:

$$47\,035 = 4 \times 10\,000 + 7 \times 1000 + 3 \times 10 + 5 \times 1$$

Comparing numbers

To compare two whole numbers, first count the digits. If they have the same number of digits, compare from the left until the digits differ.

Example 1●

Write these from smallest to largest: $3087$, $3708$, $387$, $3078$.

$387$ has only three digits, so it is smallest.

$3078 < 3087 < 3708$

Same thousands digit, so compare the hundreds, then tens.

Order: $387, 3078, 3087, 3708$.

Ancient number systems

Older systems did not use place value. The Egyptians drew a different symbol for 1, 10, 100, 1000 and so on and repeated them. The Babylonians used base 60, which is why we still have 60 minutes in an hour. Roman numerals are still seen on clocks and buildings.

Example 2●●

Write $1994$ in Roman numerals.

$1994 = 1000 + 900 + 90 + 4$

$= \text{M} + \text{CM} + \text{XC} + \text{IV} = \text{MCMXCIV}$

Flashcards

Each place is worth...

ten times the place to its right.

Expanded form of 5208

$5 \times 1000 + 2 \times 100 + 8 \times 1$

Roman numeral for 90

XC

Why 60 minutes in an hour?

The Babylonians counted in base 60.

Practice

1. What is the value of the digit $7$ in $27\,431$?

2. What is the value of the $6$ in $1\,365\,204$?

3. Which number is $3 \times 1000 + 4 \times 10 + 2$?

   $3420$$3042$$342$$30\,402$

4. Which is the largest?

   $9899$$9989$$10\,001$$9998$

5. Write XIV as a number.

6. Write XLIX as a number.

7. Which is $2024$ in Roman numerals?

   MMXXIVMMXXIIIIMMXIVXMMCCIV

8. The Babylonian number system was based on groups of what number?

Try again

More questions

New numbers every time. Keep going until you get five in a row.