Michigan Grade 5 Math

Why should the number be rounded only once?

An illustrative measurement is 34.749 centimeters. Report it to the nearest tenth of a centimeter. A student first rounds it to 34.75, then rounds that result to 34.8. Decide whether this agrees with rounding the original measurement directly. Keep the original decimal available so the requested place value can be checked.

Explain the solution

The neighboring tenths are 34.7 and 34.8. Their midpoint is 34.75. The original 34.749 lies just below that midpoint, so it is closer to 34.7. Its distance from 34.7 is 0.049, and its distance from 34.8 is 0.051. Direct rounding to the nearest tenth therefore gives 34.7 centimeters. The hundredths digit in the original decimal is four, consistent with that decision. Rounding first to the nearest hundredth produces 34.75, which has lost the information that the original measurement was below the midpoint. Rounding that intermediate value again gives a different result. Use the original value for the requested precision.

Notice the reasoning

Rounding is not simply removing the final digits. It chooses a nearby value at a stated place. Here the thousandths digit matters when explaining how the original value differs from the midpoint, even though the hundredths digit determines the usual nearest-tenth decision. Label a number line with 34.7, 34.75, and 34.8, and place 34.749 immediately to the left of the midpoint. Do not draw equal spacing between values with unequal differences. The task uses an invented measurement and a rounding convention; it makes no claim about a real instrument’s accuracy. The rounded report approximates the original rather than changing it.

Try a related task

Round 34.751 centimeters directly to the nearest tenth. It is above the same midpoint and rounds to 34.8. Compare that explanation with the first measurement. Then round both original values to the nearest hundredth: both become 34.75 even though their nearest-tenth reports differ. Ask a learner to explain which information was lost. At an exact midpoint, apply the classroom’s stated tie convention; the two original measurements here avoid a tie. Choose more decimal practice when the student can identify the requested place, neighboring values, and reason for the decision.

Selected references from Michigan mathematics standards

The Michigan mathematics standards directory links the current mathematics document, adopted by the State Board of Education in 2010 and currently linked in the state’s academic standards directory. These selected references identify the worked activity’s focus. The expectations include numbered requirements, examples, and mathematical practices. Read the full document and confirm the school’s current instructional sequence.

Sources checked October 6, 2026. Read complete requirements, clarifications, limitations, and mathematical practices alongside the school’s sequence. This selected activity is an entry point for instruction.

Connect the explanation with practice

Use the lesson, worksheet, and quiz directory to choose a related skill. The existing resource links remain available; open each activity’s directions to understand its timer, tools, question count, and scoring.

The currently linked 2025–26 state guide identifies M-STEP English language arts and mathematics in Grades 3–7, including Grade 5. Follow the school’s current assigned assessment pathway and directions. Independently published practice may use its own timer, tools, question count, and scoring; these are not official administration specifications or a prediction of a state performance level. Read the currently linked state assessment guide.

Read MDE assessment updates for later guidance. Keep one example of the student’s reasoning with the practice result. Choose a smaller model, a related question, or a new context according to the difficulty revealed in the worked activity.