Chapter 9 Exam

A mixture needs 355 milliliters from a 1-liter whole. Express the required fraction of the liter in two forms.

The assigned question is: “A mixture needs 355 milliliters from a 1-liter whole. Express the required fraction of the liter in two forms.” A learner wrote: “355 parts of the stated whole give a fraction with denominator 100, so my result is 1.355 or 71/200.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

A monitor reads 6.133 seconds. A technician moves the decimal three places right to count thousandths. What whole-number count should appear and why?

The assigned question is: “A monitor reads 6.133 seconds. A technician moves the decimal three places right to count thousandths. What whole-number count should appear and why?” A learner wrote: “6.133 × 1000 = 6134. I used this intermediate value to finish the assigned problem.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

Which quality-control threshold, 0.217 L or 0.231 L, permits the larger filling amount? Explain using aligned place values.

The assigned question is: “Which quality-control threshold, 0.217 L or 0.231 L, permits the larger filling amount? Explain using aligned place values.” A learner wrote: “I compared 0.217 only by its first digit and recorded 1.231 L.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

A tolerance sheet accepts two-decimal measurements. What number should be printed for a part measured at 4.638 cm? Explain your choice.

The assigned question is: “A tolerance sheet accepts two-decimal measurements. What number should be printed for a part measured at 4.638 cm? Explain your choice.” A learner wrote: “I rounded the recorded value 4.638 without checking the next smaller decimal place and recorded 5.64 cm.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

A record was changed from 0.232 to 23.2. Did it grow by a factor of 100 or shrink by that factor? Show a numeric check.

The assigned question is: “A record was changed from 0.232 to 23.2. Did it grow by a factor of 100 or shrink by that factor? Show a numeric check.” A learner wrote: “0.232 × 100 = 24.2. I used this intermediate value to finish the assigned problem.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

A record was changed from 0.233 to 0.0233. Did it grow by a factor of 10 or shrink by that factor? Show a numeric check.

The assigned question is: “A record was changed from 0.233 to 0.0233. Did it grow by a factor of 10 or shrink by that factor? Show a numeric check.” A learner wrote: “0.233 ÷ 10 = 1.0233. I used this intermediate value to finish the assigned problem.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

A measured segment has a label of 2660 mm. The report only allows meters. Convert and explain whether the segment is longer than 3 m.

The assigned question is: “A measured segment has a label of 2660 mm. The report only allows meters. Convert and explain whether the segment is longer than 3 m.” A learner wrote: “2660 ÷ 1000 = 3.66. I used this intermediate value to finish the assigned problem.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

Two parcels weigh 2.57 kg and 1.77 kg. A clerk estimates 5 kg combined. Test the estimate and report the exact total.

The assigned question is: “Two parcels weigh 2.57 kg and 1.77 kg. A clerk estimates 5 kg combined. Test the estimate and report the exact total.” A learner wrote: “2.57 + 1.77 = 5.34 kg. I used this sum for the two parcel masses.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.