Place value and ordering numbers

Place value of integers

Each digit's value depends on its column.

Example: in 3,452,108 the digit 4 represents 400,000.

Decimal place value

After the decimal point, columns are tenths (1/10), hundredths (1/100), thousandths (1/1000)…

In 0.728 the 7 is 7 tenths (0.7), the 2 is 2 hundredths (0.02), the 8 is 8 thousandths (0.008).

Ordering decimals

Line up the decimal points and compare column by column from left to right. Add zeros to the right where needed to give equal lengths.

Example: order 0.5, 0.45, 0.504, 0.4. Rewrite: 0.500, 0.450, 0.504, 0.400. In ascending order: 0.4, 0.45, 0.5, 0.504.

Ordering negative numbers

On a number line, numbers further left are smaller. So −7 < −3 < 0 < 4. The bigger a negative number "looks", the smaller it actually is.

Ordering fractions

Convert to a common denominator, then compare numerators. Or convert to decimals.

Example: order 3/4, 5/8, 7/10. Common denominator 40: 30/40, 25/40, 28/40. Ascending: 25/40, 28/40, 30/40 → 5/8, 7/10, 3/4.

Inequality symbols

• < less than

• greater than

• ≤ less than or equal to
• ≥ greater than or equal to

The arrow always points to the smaller value.

Common CCEA exam tip

Read carefully whether the answer should be ascending (smallest first) or descending (largest first). The mark scheme is strict on order — a correct list in the wrong direction usually loses the A1.