Place value and ordering decimals

• Each digit of a number has a place value.

• In the decimal system, the place values are all powers of 10, including hundreds, tens, units, tenths, hundredths, and thousandths.

• In every number, each place to the left is 10 times greater and each place to the right is 10 times smaller.

• The decimal point separates the whole numbers from the parts (or fractions) of a number. An understanding of place value is essential for ordering decimals.

A place value table can help to clearly show the value of each digit. To find the place value of a digit:

1. Write the number in a place value table, using the decimal point to get each digit in the correct column.

2. Read the column for the place value of the digit.

3. The value of the digit is the digit multiplied by the column heading.

Two decimal numbers can be compared in size using inequality symbols (< or >). Decimal numbers can be arranged in ascending or descending order.

To compare a list of decimal numbers:

1. Write the numbers in a place value table, lining up the decimal points to get each digit in the correct column.

2. If the numbers have a different amount of digits, there may be some gaps in the columns. Fill any gaps with a zero.

3. Compare the digits in the columns, starting at the left with the greatest place value.

4. A greater digit means that the number is greater.

5. When digits are equal in a column, move to the next column to the right and compare those digits.

With practise this can be done without the place value table, by writing the numbers lined up with their decimal points. The decimal point of a whole number comes after the last digit. Once each number is compared, they can be put in to ascending or descending order.

Practise ordering decimals and place value with these activities. You might need a pen and paper to help with your workings out.

Understanding place value and how to order decimals is useful when comparing decimals.

• Height, length and mass often include decimal numbers. A child with a height of 1∙3 metres is taller than another with a height of 1∙09 metres.

• In a race, athletes are ranked in descending order from first place to last place. When comparing the speeds of athletes, their times are recorded to the nearest thousandth of a second and placed or ranked in ascending order (fastest time first).