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Choose one of the scientific numbers from the list and divide it by 0.3 (or

divide 0.3 by the number you choose). Show your work.

11 answers

Sure! Let's choose the scientific number \(6.02 \times 10^{23}\), which is Avogadro's number, often used in chemistry.

We'll divide Avogadro's number by 0.3:

\[ \text{Calculation: } \frac{6.02 \times 10^{23}}{0.3} \]

  1. First, represent \(0.3\) as a fraction: \(0.3 = \frac{3}{10}\).
  2. Now, rewrite the division:

\[ \frac{6.02 \times 10^{23}}{0.3} = 6.02 \times 10^{23} \div \frac{3}{10} = 6.02 \times 10^{23} \times \frac{10}{3} \]

  1. Multiply \(6.02\) by \(10\):

\[ 6.02 \times 10 = 60.2 \]

  1. Now we have:

\[ \frac{60.2 \times 10^{23}}{3} \]

  1. Next, divide \(60.2\) by \(3\):

\[ 60.2 \div 3 \approx 20.0667 \]

  1. Thus:

\[ \frac{60.2}{3} \approx 20.0667 \]

  1. Therefore, multiplying by \(10^{23}\):

\[ 20.0667 \times 10^{23} \]

  1. We can express this in scientific notation:

\[ = 2.00667 \times 10^{24} \]

So, \( \frac{6.02 \times 10^{23}}{0.3} \approx 2.00667 \times 10^{24} \).

In this problem, you will practice adding, subtracting, multiplying, and dividing numbers written in scientific notation. For each part, use the following numbers.
3.2×104
1.95×106
8.03×10−8
2.56×10−2
4.82×1012

Choose one of the scientific numbers from the list and divide it by 0.3 (or
divide 0.3 by the number you choose). Show your work.

Let's choose the scientific number \(4.82 \times 10^{12}\) and divide it by \(0.3\).

Steps to Divide \(4.82 \times 10^{12}\) by \(0.3\):

  1. Set up the division:

\[ \frac{4.82 \times 10^{12}}{0.3} \]

  1. Convert \(0.3\) to a fraction:

\[ 0.3 = \frac{3}{10} \]

  1. Rewrite the division:

\[ \frac{4.82 \times 10^{12}}{0.3} = 4.82 \times 10^{12} \div \frac{3}{10} = 4.82 \times 10^{12} \times \frac{10}{3} \]

  1. Multiply \(4.82\) by \(10\):

\[ 4.82 \times 10 = 48.2 \]

  1. Now we have:

\[ \frac{48.2 \times 10^{12}}{3} \]

  1. Now divide \(48.2\) by \(3\):

\[ 48.2 \div 3 \approx 16.0667 \]

  1. Combine with \(10^{12}\):

\[ \frac{48.2}{3} \approx 16.0667 \implies 16.0667 \times 10^{12} \]

  1. Convert to scientific notation:

To express \(16.0667\) in scientific notation, we shift the decimal point to the left by one place:

\[ 16.0667 = 1.60667 \times 10^1 \]

Thus,

\[ 16.0667 \times 10^{12} = 1.60667 \times 10^{13} \]

Final Result

So,

\[ \frac{4.82 \times 10^{12}}{0.3} \approx 1.60667 \times 10^{13} \]

plain languge

Sure! Let me explain the process in simpler terms.

Goal: Divide \(4.82 \times 10^{12}\) by \(0.3\)

  1. Write down the numbers: You have \(4.82 \times 10^{12}\) (a very large number) and you want to divide it by \(0.3\) (a smaller number).

  2. Change \(0.3\) to a fraction: Instead of using \(0.3\), we can think of it as \(\frac{3}{10}\). This makes it easier to understand how to divide.

  3. Rearrange the division: Dividing by a fraction is the same as multiplying by its reciprocal (flipping it over). So, we can change: \[ \frac{4.82 \times 10^{12}}{0.3} \text{ to } 4.82 \times 10^{12} \times \frac{10}{3} \]

  4. Multiply \(4.82\) by \(10\): When you multiply \(4.82\) by \(10\), you move the decimal point: \[ 4.82 \times 10 = 48.2 \]

  5. Now divide by \(3\): Next, take \(48.2\) and divide it by \(3\): \[ 48.2 \div 3 \approx 16.0667 \]

  6. Combine it back with \(10^{12}\): Now, we put \(16.0667\) together with \(10^{12}\): \[ 16.0667 \times 10^{12} \]

  7. Convert to scientific notation: To write \(16.0667\) in scientific notation, shift the decimal to the left one place: \[ 16.0667 = 1.60667 \times 10^1 \] So multiplying by \(10^{12}\) gives you: \[ 1.60667 \times 10^1 \times 10^{12} = 1.60667 \times 10^{13} \]

Final Answer:

Thus, when you divide \(4.82 \times 10^{12}\) by \(0.3\), you get approximately: \[ 1.60667 \times 10^{13} \]

This represents a very large number!

put it in plain language

Absolutely! Here's a breakdown in very simple terms:

Task: Divide \(4.82 \times 10^{12}\) by \(0.3\)

  1. Understand the numbers:

    • You have a big number: \(4.82\) followed by \(12\) zeros (which is \(4,820,000,000,000\)).
    • You want to divide this big number by \(0.3\) (which is less than \(1\)).

  2. Change \(0.3\) into a fraction:

    • Instead of using \(0.3\), think of it as a fraction: \(0.3\) is the same as \(\frac{3}{10}\).

  3. Change how you do the math:

    • Dividing by \(\frac{3}{10}\) is the same as multiplying by \(\frac{10}{3}\). So now it looks like this: \[ 4.82 \times 10^{12} \times \frac{10}{3} \]

  4. Multiply \(4.82\) by \(10\):

    • If you multiply \(4.82\) by \(10\), you just move the decimal point one place to the right. So, \(4.82\) becomes \(48.2\).

  5. Divide \(48.2\) by \(3\):

    • Now, divide \(48.2\) by \(3\). That gives you about \(16.07\) (which is a little more than \(16\)).

  6. Bring back the \(10^{12}\):

    • Now, take \(16.07\) and write it with the \(10^{12}\) you had before. So it looks like this: \(16.07 \times 10^{12}\).

  7. Convert to scientific notation:

    • To write \(16.07\) in scientific notation, move the decimal one spot to the left: \(16.07\) becomes \(1.607\) and you add \(1\) to the exponent of \(10^{12}\) (making it \(10^{13}\)).
    • So now, it’s \(1.607 \times 10^{13}\).

Final Result:

So, when you divide \(4.82 \times 10^{12}\) by \(0.3\), you get about \(1.607 \times 10^{13}\).

That's still a really big number!

get rid of the }, ], *, and \

Sure! Here’s the explanation without any special symbols:

Task: Divide 4.82 times 10 to the 12 by 0.3

  1. Understand the numbers:

    • You have a big number: 4.82 followed by 12 zeros (which is 4,820,000,000,000).
    • You want to divide this big number by 0.3 (which is less than 1).

  2. Change 0.3 into a fraction:

    • Instead of using 0.3, think of it as a fraction: 0.3 is the same as 3 over 10.

  3. Change how you do the math:

    • Dividing by 3 over 10 is the same as multiplying by 10 over 3. So now it looks like this:

    4.82 times 10 to the 12 times 10 over 3

  4. Multiply 4.82 by 10:

    • If you multiply 4.82 by 10, you just move the decimal point one place to the right. So, 4.82 becomes 48.2.

  5. Divide 48.2 by 3:

    • Now, divide 48.2 by 3. That gives you about 16.07 (which is a little more than 16).

  6. Bring back the 10 to the 12:

    • Now, take 16.07 and write it with the 10 to the 12 that you had before. So it looks like this: 16.07 times 10 to the 12.

  7. Convert to scientific notation:

    • To write 16.07 in scientific notation, move the decimal one spot to the left: 16.07 becomes 1.607 and you add 1 to the exponent of 10 to the 12 (making it 10 to the 13).
    • So now, it is 1.607 times 10 to the 13.

Final Result:

So, when you divide 4.82 times 10 to the 12 by 0.3, you get about 1.607 times 10 to the 13.

That's still a really big number!

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