## Decimal place value (Level 4)

Ragged decimals are those that have varying numbers of digits to the right of the decimal point. At the decimal place value level the student can successfully compare the value of ‘ragged decimals’ (e.g. one decimal place compared to two or three decimal places) without needing to equalise the number of decimal places. Based on this multi-unit understanding of decimal place value, the student can readily multiply or divide decimals by multiples of ten or one hundred. This level of understanding decimals is less common than often thought. For example, in the National Assessment Program in 2010, only 47% of Year 7 students in Australia could correctly multiply 37.9 x 10 without a calculator. In total, 25% appended a zero to the end to answer 37.90 and another 21% selected the answer 3790.

Although 0.24 may be thought of as “two tenths and four hundredths” using a positional tags approach, in comparing 0.24 with, say, 0.08, it is more helpful to regard 0.24 as equivalent to 24 hundredths.

Which is the biggest number, 0.75 or 0.8?

It is not unusual for students to invent a range of nonstandard ways of symbolising decimals, such as three-hundredths. Students’ recordings of three-hundredths include variations such as 0.300 and 3.00. Both of these recordings reflect an attachment to the whole number three hundred, transferred to a decimal setting.

Comparing the magnitude of decimals with different lengths, such as comparing decimals recorded to 3 decimal places with decimals recorded to 2 decimal places, can highlight anomalies in the ways students interpret decimals as can be seen in the following explanation.

Comparing the size of decimals displaying whole number thinking (Year 5)