Powers of 10 and place value to thousandths Transitional Reasoning Practice

Questions

1. 1.

   An optical inspection camera in an electronics lab displays the apparent width of a miniature circuit component as 0.064 millimeters at its baseline setting. To examine the component more closely, a technician first magnifies the image by a factor of $10^3$. The technician then adjusts the focus, which reduces the magnified display width to $\frac{1}{10}$ of that magnified size. What is the final display width of the component, and how many times greater is the value of the digit 6 in this final width than in the baseline width?

   • A) 64 millimeters, and the value of the digit 6 is $10^3$ times greater
   • B) 6.4 millimeters, and the value of the digit 6 is 10 times greater
   • C) 6.4 millimeters, and the value of the digit 6 is $10^2$ times greater
   • D) 0.64 millimeters, and the value of the digit 6 is 10 times greater
2. 2.

   A biomedical engineer inspects four batches of micro-wire to find which batch meets a target strand thickness. To be approved, the thickness of a single strand must be greater than 0.375 millimeters but less than 0.38 millimeters. The total thickness of sample strands from each batch is measured: Batch A has 10 strands measuring 3.71 millimeters, Batch B has $10^2$ strands measuring 37.4 millimeters, Batch C has $10^3$ strands measuring 378 millimeters, and Batch D has $10^2$ strands measuring 38.3 millimeters. Which batch meets the approval requirement?

   • A) Batch A
   • B) Batch B
   • C) Batch C
   • D) Batch D
3. 3.

   An automated compounding device in a hospital pharmacy prepares pediatric antibiotic suspensions. The device starts with a concentrated base volume of 30.75 milliliters and dilutes it so that each single dose is $\frac{1}{10}$ of this volume. To program the dispensing verification code, the pharmacist must enter the single dose in expanded form using powers of 10. Which expression correctly represents the single dose in milliliters?

   • A) $3 \times 10^0 + 7 \times \left(\frac{1}{10^1}\right) + 5 \times \left(\frac{1}{10^2}\right)$
   • B) $3 \times 10^0 + 7 \times \left(\frac{1}{10^2}\right) + 5 \times \left(\frac{1}{10^3}\right)$
   • C) $3 \times 10^1 + 7 \times \left(\frac{1}{10^1}\right) + 5 \times \left(\frac{1}{10^2}\right)$
   • D) $3 \times 10^0 + 7 \times \left(\frac{1}{10^1}\right) + 5 \times \left(\frac{1}{10^3}\right)$
4. 4.

   A meteorology station records atmospheric pressure anomalies using sensitive digital sensors, where Sensor A records a base anomaly of 4.5 units. In the calibration process, the reading of Sensor B is calculated by dividing Sensor A's reading by $10^2$. Sensor C is then configured so that the value of the digit 4 is $\frac{1}{10}$ of its value in Sensor B, while the value of the digit 5 is 10 times its value in Sensor B. What is the reading recorded by Sensor C?

   • A) 0.504
   • B) 0.450
   • C) 0.054
   • D) 0.045
5. 5.

   An environmental scientist records the mass of a microscopic fiber as 0.076 grams. For an experimental composite material, this mass is scaled by a factor of $10^3$ and then combined with an additive that has a mass of 4 tenths and 9 thousandths of a gram. What is the total mass, in grams, of the resulting composite sample?

   • A) 76.409 grams
   • B) 76.490 grams
   • C) 7.649 grams
   • D) 76.049 grams

Answers and step-by-step solutions appear after you finish the test.