Here are two decimals: 0.6 and 0.405.

Hands up: which one do you think is bigger? Trust your first gut answer, then hold that thought. Some people's gut says 0.405, because it has more digits. Is a longer decimal always the bigger one?

The place-value chart lines each pair of decimals up column by column. Watch which column decides the winner each time. Longer is not always bigger.

Today we sort a set of decimals into order from smallest to largest: 0.4, 0.404, 0.44 and 0.044. They all use the same digits, so we cannot judge by looks. We line up the point and read from the left, column by column, until we can place each one.

Predict where each card lands before we drop it in. Do not judge by how many digits each one has.

Today we work through these ordering rounds together, each one a step trickier than the last: first a set with clear tenths, then a set where the tenths tie and we must read the hundredths, then a set with a trailing-zero trap, and finally we order a set right down to thousandths: 0.452, 0.4, 0.45, 0.455.

After Round 4, we pause on two neighbours from that set, 0.45 and 0.455, and find a decimal that sits strictly between them.