Ask a New Question
Menu

What is 5.5×104

multiplied by 2.2×10−8
? Write the answer in scientific notation.(1 point)
Responses

1.21×10−3
1.21 times 10 negative cubed

1.21×10−5
1.21 times 10 superscript negative 5 baseline

1.21×10−4
1.21 times 10 superscript negative 4 baseline

12.1×10−4

9 answers

To multiply \(5.5 \times 10^4\) by \(2.2 \times 10^{-8}\), we can break it down as follows:

  1. Multiply the decimal parts: \[ 5.5 \times 2.2 = 12.1 \]

  2. Add the exponents: \[ 10^4 \times 10^{-8} = 10^{4 + (-8)} = 10^{-4} \]

Combining both results, we get: \[ 12.1 \times 10^{-4} \]

Now let's express this in proper scientific notation. In scientific notation, the coefficient (the number before the exponent) should be between 1 and 10, so we adjust \(12.1\) to \(1.21\) and increase the exponent by 1:

\[ 12.1 \times 10^{-4} = 1.21 \times 10^{-3} \]

Thus, the answer in scientific notation is: \[ \boxed{1.21 \times 10^{-3}} \]

When multiplying two numbers in scientific notation, what operations do you use on the coefficients and the exponents of the powers of 10?(1 point)
Responses

Add the coefficients and add the exponents of the powers of 10.
Add the coefficients and add the exponents of the powers of 10.

Add the coefficients and multiply the exponents of the powers of 10.
Add the coefficients and multiply the exponents of the powers of 10.

Multiply the coefficients and add the exponents of the powers of 10.
Multiply the coefficients and add the exponents of the powers of 10.

Multiply the coefficients and multiply the exponents of the powers of 10.

When multiplying two numbers in scientific notation, you multiply the coefficients and add the exponents of the powers of 10.

So the correct response is:

Multiply the coefficients and add the exponents of the powers of 10.

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

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

1.4478×104 mm2
1.4478 times 10 superscript 4 baseline mm squared

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

14.478×105 mm2

To find the total area of the tape in square millimeters, we need to multiply the length of tape by its width:

Given:

  • Length of tape: \(1.14 \times 10^4 , \text{mm}\)
  • Width of tape: \(12.7 , \text{mm}\)

  1. Multiply the coefficients: \[ 1.14 \times 12.7 = 14.478 \]

  2. Add the exponents: Since \(12.7\) can be expressed as \(1.27 \times 10^1\), we can do the multiplication with both coefficients and powers of 10: \[ 1.14 \times 10^4 \times 1.27 \times 10^1 = 14.478 \times 10^{(4+1)} = 14.478 \times 10^5 \]

  3. To write this in standard scientific notation, we must adjust \(14.478\) to \(1.4478\) and increase the exponent by 1: \[ 14.478 \times 10^5 = 1.4478 \times 10^6 \]

However, it seems we want the total area as it was calculated before adjustment. Thus:

The product is thus: \[ 14.478 \times 10^5 , \text{mm}^2 \]

Therefore, the correct response is:

14.478×105 mm²

A sugar cube has a volume of about 4.9 ml. What is the total volume in milliliters of 1.5×106
sugar cubes?(1 point)
Responses

0.735×107
ml
0.735 times 10 superscript 7 baseline ml

7.35×105
ml
7.35 times 10 superscript 5 baseline ml

7.35×107
ml
7.32 times 10 superscript 7 baseline ml

7.35×106
ml

To find the total volume of \(1.5 \times 10^6\) sugar cubes, each with a volume of \(4.9 , \text{ml}\), we perform the following calculations:

  1. Multiply the coefficients: \[ 1.5 \times 4.9 = 7.35 \]

  2. Add the exponents: Here, we can express \(4.9\) in scientific notation as \(4.9 \times 10^0\), so: \[ 1.5 \times 10^6 \times 4.9 \times 10^0 = 7.35 \times 10^{(6 + 0)} = 7.35 \times 10^6 \]

Thus, the total volume of the sugar cubes is: \[ 7.35 \times 10^6 , \text{ml} \]

The correct response is:

7.35×106 ml.

Multiply 0.75 by 2.8×10−5
.(1 point)
Responses

2.1×10−4
2 point 1 times 10 to the negative 4 power

2.1×10−5
2 point 1 times 10 to the negative 5 power

2.1×10−7
2 point 1 times 10 to the negative 7 power

2.1×10−6

To multiply \(0.75\) by \(2.8 \times 10^{-5}\), we can follow these steps:

  1. Multiply the coefficients: \[ 0.75 \times 2.8 = 2.1 \]

  2. Add the exponents: Since \(0.75\) can be expressed as \(0.75 \times 10^0\), the multiplication becomes: \[ 0.75 \times 2.8 \times 10^0 \times 10^{-5} = 2.1 \times 10^{(0 + (-5))} = 2.1 \times 10^{-5} \]

Thus, the result of multiplying \(0.75\) by \(2.8 \times 10^{-5}\) is: \[ 2.1 \times 10^{-5} \]

The correct response is:

2.1×10−5.