1. What is 5.5 x 10^4 multiplied by 2.2 x 10^-8? Write the answer in scientific notation.

Question

A. 12.1 x 10^-4
B. 1.21 x 10^-3
C. 1.21 x 10^-4
D. 1.21 x 10^-5
2. When multiplying two numbers in scientific notation, what operations do you use on the coefficients and the exponents of the powers of 10?
A. Multiply the coefficients and multiply the exponents of the powers of 10.
B. Add the coefficients and add the exponents of the powers of 10.
C. Multiply the coefficients and add the exponents of the powers of 10.
D. Add the coefficients and multiply the exponents of the powers of 10.
3. A tape dispenser holds 1.14 x 10^4 mm of tape that is 12.7 mm wide. Multiply the two numbers to find the total area in square millimeters of tape. Write the product in scientific notation.
A. 14.478 x 10^4 mm^2
B. 1.448 x 10^5 mm^2
C. 14.478 x 10^5 mm^2
D. 1.4478 x 10^4 mm^2
4. A sugar cube has a volume of about 4.9 ml. What is the total volume of milliliters of 1.5 x 10^6 sugar cubes?
A. 7.35 x 10^5 ml
B. 7.35 x 10^7 ml
C. 0.735 x 10^7 ml
D. 7.35 x 10^5 ml
5. Multiply 0.75 by 2.8 x 10^-5
A. 2.1 x 10^-6
B. 2.1 x 10^-4
C. 2.1 x 10^-7
D. 2.1 x 10^-5

Answer 1

Let's solve each of these questions one by one.

1. To multiply \(5.5 \times 10^4\) by \(2.2 \times 10^{-8}\):

   • Multiply the coefficients: \(5.5 \times 2.2 = 12.1\)
   • Add the exponents: \(4 + (-8) = -4\)
   • Therefore, the answer is \(12.1 \times 10^{-4}\).
   • In scientific notation, this becomes \(1.21 \times 10^{-3}\).
   • Answer: B. 1.21 x 10^-3

2. When multiplying two numbers in scientific notation:

   • Multiply the coefficients and add the exponents of the powers of 10.
   • Answer: C. Multiply the coefficients and add the exponents of the powers of 10.

3. To find the total area of tape, multiply \(1.14 \times 10^4\) mm by \(12.7\) mm:

   • Multiply the coefficients: \(1.14 \times 12.7 = 14.478\)
   • The power of ten remains \(10^4\).
   • Therefore, the area is \(14.478 \times 10^4\).
   • In scientific notation, this is \(1.4478 \times 10^5\).
   • Answer: B. 1.448 x 10^5 mm^2

4. To find the total volume of \(1.5 \times 10^6\) sugar cubes, each with a volume of about \(4.9\) ml:

   • Multiply the coefficients: \(4.9 \times 1.5 = 7.35\)
   • The power of ten remains \(10^6\).
   • Therefore, the total volume is \(7.35 \times 10^6\) ml.
   • Answer: B. 7.35 x 10^7 ml

5. To multiply \(0.75\) by \(2.8 \times 10^{-5}\):

   • Multiply the coefficients: \(0.75 \times 2.8 = 2.1\)
   • The power of ten remains \(10^{-5}\).
   • Therefore, the answer is \(2.1 \times 10^{-5}\).
   • Answer: D. 2.1 x 10^-5

Summary of Answers:

1. B. 1.21 x 10^-3
2. C. Multiply the coefficients and add the exponents of the powers of 10.
3. B. 1.448 x 10^5 mm^2
4. B. 7.35 x 10^7 ml
5. D. 2.1 x 10^-5

Answer 2

A tape dispenser holds 1.14×104 mm of tape that is 12.7 mm wide. Multiply the two numbers to find the total area in square millimeters of tape. Write the product in scientific notation.(1 point)
Responses

14.478×105 mm2
14.478 times 10 superscript 5 baseline mm squared

14.478×104 mm2
14.478 times 10 superscript 4 baseline mm squared

1.4478×105 mm2
1.4478 times 10 superscript 5 baseline mm squared

1.4478×104 mm2

Answer 3

To find the total area of the tape, we need to multiply the length of the tape, \(1.14 \times 10^4\) mm, by its width, \(12.7\) mm.

Step 1: Multiply the coefficients:

• \(1.14 \times 12.7 = 14.478\)

Step 2: Consider the power of ten:

• Since the width (12.7 mm) has no exponent, you can consider it as \(12.7 \times 10^0\).
• Therefore, the power of ten remains consistent with the length: \(10^4\).

Step 3: Combine the results:

• We have \(14.478 \times 10^4\) mm².

Step 4: Convert to scientific notation:

• To express \(14.478\) in proper scientific notation, we convert it to \(1.4478\) and adjust the power of ten:
  • \(14.478 \times 10^4 = 1.4478 \times 10^5\).

Thus, the total area in scientific notation is \(1.4478 \times 10^5\) mm².

Final Answer:

1.4478×10^5 mm²