Place Value & Ordering

Every digit in a number has a value that depends on its position, not just what the digit is. In 27 463, the 7 sits in the thousands column, so it is worth 7000, not 7.

The same idea applies after the decimal point. In 6.548, the 4 sits in the hundredths column, so it is worth 0.04. Each column to the right of the decimal point is ten times smaller than the one before it: tenths, then hundredths, then thousandths.

Converting a number to words means reading off each group of digits and naming its column, for example 4608 is "four thousand, six hundred and eight".

Converting words back to figures is where marks are most often dropped, because a "missing" place value needs a placeholder zero. "Nineteen thousand and fifteen" is 19015, not 19150, because there are no hundreds or tens beyond the thousands, so a 0 has to sit in that column.

On a number line, numbers get larger as you move right and smaller as you move left. This means negative numbers can be counterintuitive: -12 is smaller than -3, even though 12 is bigger than 3, because -12 sits further to the left.

A safe method is to picture, or sketch, a number line and place each value on it before writing the final order.

The safest way to order decimals is to line up the decimal points and compare column by column, tenths first, then hundredths, then thousandths, exactly like ordering whole numbers by their place value.

A common trap is judging size by how many digits a decimal has. 0.096 looks like a "bigger" number than 0.6 because it has more digits, but 0.6 is six tenths, while 0.096 is less than one tenth, so 0.6 is much larger.