Ranking Masses on a Scale That Overreports Precision
During a fifth-grade science unit on mass, three teams weigh their rock samples on a digital scale that displays mass to the nearest thousandth of a kilogram. Team A's tray reads 2.48 kg, Team B's tray reads 2.408 kg, and Team C's tray reads 2.5 kg. Before the samples go back into storage, the trays must be lined up from lightest to heaviest. The scale manual warns that readings are only reliable to the nearest hundredth of a kilogram, so digits beyond the hundredths place should not be trusted. Jordan argues that Team B's tray is heaviest because "408 is bigger than 48 and bigger than 5." Priya argues that Team C is heaviest because "it has the fewest digits after the decimal point, so the 5 sits in the biggest place." The class must settle the order, decide how the scale's limited precision affects the recorded masses, and report the combined mass on a recycling form that accepts hundredths only.
1. Determine the correct order of the three masses from least to greatest, and evaluate both Jordan's and Priya's reasoning.
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Give every mass the same number of decimal places so the digits line up: 2.480, 2.408, 2.500.
Compare place by place from the left. All three have 2 ones. In the tenths place the digits are 4, 4, and 5, so Team C (2.500) is the greatest. A and B tie in tenths (4), so move to hundredths: A has 8 and B has 0, so 2.480 > 2.408.
Least to greatest: 2.408 < 2.48 < 2.5.
- Jordan compared the decimal digits as if they were whole numbers. 408 thousandths is less than 480 thousandths because the 4 in 2.408 sits in the tenths place, not the hundreds place.
- Priya reached the right answer for the wrong reason. Counting digits is not a rule: 2.5 > 2.05 even though 2.05 has more digits. 2.5 is greatest here only because its tenths digit is 5.
2. The scale is reliable only to the nearest hundredth of a kilogram. Round each mass to the nearest hundredth and explain whether rounding changes the ranking.
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2.48 → 2.48 kg (already at hundredths). 2.408 → 2.41 kg: the thousandths digit is 8, which is 5 or more, so the hundredths digit 0 rounds up to 1. 2.5 → 2.50 kg: same value, written with hundredths.
The rounded order is 2.41 < 2.48 < 2.50, identical to the unrounded order. Rounding moved Team B up by 0.002 kg, but Team A was already ahead of B by 0.072 kg, so the gap (about 0.07 kg) survives rounding. Anyone who rounded first and then ranked would still get the correct order here, but the safest habit is to rank and compute with the original readings and round only for reporting.
3. Report the combined mass of the three trays to the nearest hundredth of a kilogram. Show the addition and explain at what point rounding should happen.
Read the worked answer
Add the unrounded readings, then round once:
2.48 + 2.408 = 4.888 4.888 + 2.5 = 7.388 kg
The thousandths digit is 8, so 7.388 rounds to 7.39 kg.
Rounding at the end is preferable because each rounding step can push the total in the same direction. Here, rounding Team B to 2.41 first gives 2.48 + 2.41 + 2.50 = 7.39, the same answer, but that agreement is luck of the digits, not a guarantee. A student who answered 7.388 would be reporting a precision the scale cannot support, since the thousandths digit is exactly what the manual says to distrust.