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Divide 3.3×104 by 5.5×107

.(1 point)
Responses

6×10−5
6 times 10 to the negative 5 power

6×10−4
6 times 10 to the negative 4 power

6×10−3
6 times 10 to the negative 3 power

6×10−6

7 answers

To divide \( 3.3 \times 10^4 \) by \( 5.5 \times 10^7 \), you follow these steps:

  1. Divide the coefficients (the numbers in front):
    \[ \frac{3.3}{5.5} = 0.6 \]

  2. Subtract the exponents of ten:
    \[ 10^{4-7} = 10^{-3} \]

  3. Combine the results:
    \[ 0.6 \times 10^{-3} \]

  4. To express this in standard scientific notation, we need a coefficient between 1 and 10. So we adjust \( 0.6 \) to \( 6 \) by moving the decimal point one place to the right, which means we have to subtract 1 from the exponent:
    \[ 6 \times 10^{-4} \]

Thus, the final answer is:

6×10−4 (6 times 10 to the negative 4 power)

are u sure

Let’s go through the calculation step-by-step to ensure accuracy:

  1. Start with the expression:
    \[ \frac{3.3 \times 10^4}{5.5 \times 10^7} \]

  2. Divide the coefficients:
    \[ \frac{3.3}{5.5} = 0.6 \]

  3. Now, handle the powers of ten:
    \[ \frac{10^4}{10^7} = 10^{4-7} = 10^{-3} \]

  4. Combine the results:
    \[ 0.6 \times 10^{-3} \]

  5. To express \( 0.6 \) in proper scientific notation (which requires a coefficient between 1 and 10), we can write it as:
    \[ 6.0 \times 10^{-4} \] Here, we moved the decimal to the right (from 0.6 to 6.0) and adjusted the exponent accordingly (from \( -3 \) to \( -4 \)).

Therefore, the correct answer is indeed:
6×10−4 (6 times 10 to the negative 4 power).

Thank you for your patience!

A city lunch program for seniors received a grant of 1.925×106 dollars. Divide that figure by the cost of $2.75 per lunch to find out how many senior lunches the grant can provide. Write the answer in scientific notation.(1 point)
Responses

7×106
7 times 10 superscript 6 baseline

0.7×106
0.7 times 10 superscript 6 baseline

0.7×105
0.7 times 10 superscript 5 baseline

7×105

To determine how many senior lunches the grant can provide, we need to divide the total grant amount by the cost per lunch.

  1. Total grant amount: \(1.925 \times 10^6\) dollars
  2. Cost per lunch: \(2.75\) dollars

Now, let's perform the division:

\[ \frac{1.925 \times 10^6}{2.75} \]

  1. Convert \(2.75\) to scientific notation:
    \[ 2.75 = 2.75 \times 10^0 \]

Now we can perform the division of coefficients and the division of powers of ten:

  1. Calculate the coefficients:
    \[ \frac{1.925}{2.75} \approx 0.7 \]

  2. Powers of ten:
    The power of ten will not change since we are dividing by \(10^0\): \[ 10^{6 - 0} = 10^{6} \]

  3. Combining these results:
    \[ 0.7 \times 10^{6} \]

  4. Convert to proper scientific notation:

While \(0.7 \times 10^6\) is technically correct, to express it in a more standard scientific notation, we would write it as:

\[ 7.0 \times 10^{5} \]

Thus, the answer represented in the form of the options provided is:

7×10^5 (7 times 10 to the fifth power).

u sure

Let's carefully go through the calculation step-by-step again to ensure we have the correct result.

  1. Total Grant Amount: \(1.925 \times 10^6\) dollars
  2. Cost per Lunch: \(2.75\) dollars

We are dividing the total grant amount by the cost per lunch:

\[ \frac{1.925 \times 10^6}{2.75} \]

Step 1: Divide the coefficients:

\[ \frac{1.925}{2.75} \approx 0.7 \]

Step 2: The power of ten remains:

\[ 10^6 \text{ (since we are dividing by \(10^0\))} \]

Step 3: Combine the results:

\[ 0.7 \times 10^6 \]

Step 4: Express \(0.7 \times 10^6\) in standard scientific notation:

Since \(0.7\) is not between \(1\) and \(10\), we can convert this to:

\[ 7.0 \times 10^{5} \]

This indeed means:

\[ 0.7 \times 10^6 = 7.0 \times 10^5 \]

To compare with your original answer options, here’s what we have:

  • \(7 \times 10^6\)
  • \(0.7 \times 10^6\) (this option is correct but is not in standard form)
  • \(0.7 \times 10^5\)
  • \(7 \times 10^5\) (this is in correct standard scientific notation)

So, the final answer that is both calculated correctly and expressed in proper scientific notation is:

7×10^5 (not \(0.7 \times 10^6\) because it is not in proper scientific notation).

Thank you for your patience, and yes, I'm sure of this result!