Powers of 10 and place value to thousandths Transitional Reasoning Download PDF

Questions

1. 1.

   An agricultural seed facility uses an automated dispenser to divide a bulk container of 84.5 grams of specialty flower seeds equally into $10^2$ sample packets. A quality control technician programs a digital sensor to verify the exact mass of each individual packet using expanded place-value notation. Which expression represents the correct mass, in grams, of one sample packet?

   • A) $(8 \times 10^0) + (4 \times \frac{1}{10^1}) + (5 \times \frac{1}{10^2})$
   • B) $(8 \times \frac{1}{10^1}) + (4 \times \frac{1}{10^3}) + (5 \times \frac{1}{10^2})$
   • C) $(8 \times \frac{1}{10^1}) + (4 \times \frac{1}{10^2}) + (5 \times \frac{1}{10^3})$
   • D) $(8 \times \frac{1}{10^2}) + (4 \times \frac{1}{10^1}) + (5 \times \frac{1}{10^3})$
2. 2.

   A laboratory technician prepares a chemical mixture using a baseline compound with a mass of 0.027 grams. In the first preparation step, the mass of this compound is increased by multiplying it by $10^1$. In the second step, the technician adds 0.15 grams of a liquid reagent and 8 thousandths of a gram of a powdered catalyst to the mixture. What is the total mass, in grams, of the final combined mixture?

   • A) 0.185 grams
   • B) 0.293 grams
   • C) 0.428 grams
   • D) 0.500 grams
3. 3.

   A robotics student programs an autonomous cart to travel along a marked testing track. The cart's guidance software calculates the distance in meters using three base-ten registers: Register 1 stores $4 \times 10^0$ meters, Register 2 stores $6 \times \frac{1}{10^1}$ meters, and Register 3 stores $9 \times \frac{1}{10^3}$ meters. The student discovers that the cart was supposed to travel a target distance of 4.690 meters instead of the currently programmed amount. Which change to Register 3 will correct the programmed distance so that the cart travels exactly 4.690 meters?

   • A) Multiply the value of Register 3 by $10^2$ so that it represents $9 \times \frac{1}{10^1}$ meters.
   • B) Multiply the value of Register 3 by $10^1$ so that it represents $9 \times \frac{1}{10^2}$ meters.
   • C) Divide the value of Register 3 by $10^1$ so that it represents $9 \times \frac{1}{10^4}$ meters.
   • D) Multiply the value of Register 3 by $10^3$ so that it represents $9 \times 10^0$ meters.
4. 4.

   A laboratory technician calibrates an analytical balance that records chemical additives to the nearest thousandth of a gram. The initial readout displays a mass of 0.315 grams. To reach the target formulation, the machine adjusts the components so that the value of the digit 5 increases by a factor of $10^2$, the value of the digit 3 decreases to $\frac{1}{10^2}$ of its initial value, and the digit 1 maintains its original place value. What is the calibrated target mass shown on the balance?

   • A) 0.153 grams
   • B) 0.513 grams
   • C) 5.013 grams
   • D) 0.351 grams
5. 5.

   An environmental monitor records an air particulate concentration of 0.084 milligrams per cubic meter. To calibrate the data stream, an automated program first multiplies this reading by $10^3$ and then divides the result by $10^1$. Which statement correctly describes the value of the digit 8 in the final calibrated reading compared to its value in the original reading?

   • A) The value of the digit 8 in the final reading is 8 tenths, which is $10^1$ times its value of 8 hundredths in the original reading.
   • B) The value of the digit 8 in the final reading is 8 tens, which is $10^3$ times its value of 8 hundredths in the original reading.
   • C) The value of the digit 8 in the final reading is 8 ones, which is $10^1$ times its value of 8 tenths in the original reading.
   • D) The value of the digit 8 in the final reading is 8 ones, which is $10^2$ times its value of 8 hundredths in the original reading.