Using Operations with Scientific Notations

Using Operations with Scientific Notations exercise

• Calculate the standard form multiplication.

  Hints

  To make it easier rearrange it.

  $2\times4$ and $10^{3}\times10^{5}$

  When multiplying indices with the same base we ADD the powers.

  $2\times4 = 8$

  $8\times(10^{3}\times10^{5})$

  Finish by putting your answer in standard form.

  Solution

  $8\times10^{8}$

  • Multiply $2$ and $4$ together
  • Add the powers $3$ and $5$ = $10^{8}$

• Calculate the standard form division

  Hints

  To make it easier rearrange it.

  $9\div3$ and $10^{7}\div10^{5}$

  When dividing indices with the same base we subtract the powers.

  $9\div3 = 3$

  $3\times(10^{7}\div10^{5})$

  Finish by putting your answer in standard form.

  Solution

  $3\times10^{2}$

  • Divide $9$ by $3$
  • Subtract the powers $7$ and $5$ = $10^{2}$

• Find the product of two values in standard form

  Hints

  To make it easier rearrange it.

  $4\times6$ and $10^{8}\times10^{4}$

  When multiplying indices with the same base we ADD the powers.

  $4\times6 = 24$

  $24\times(10^{8}\times10^{4}) = 24\times10^{12}$ (We add the powers here)

  The answer is not in standard form.

  For this $24$ needs to be a number between $1$ and $10$ but this means we have to add one more to the indices.

  Solution

  $2.4\times10^{13}$ in standard form.

• Calculate and leave the answer in standard form.

  Hints

  Some of the answers will need putting into standard form when the calculation has been done.

  For example, if the answer is $27\times10^{3}$, we need to write it as a number between $1$ and $10$ and make adjustments.

  $2.7\times10^{4}$

  If the answer is already a number between $1$ and $10$ then no adjustment is necessary it is in standard form.

  Solution

  • $(45\times10^{6})\div(3\times10^{2}) = 1.5\times10^{5}$

  You can see this explained in detail above.

  • $(7\times10^{3})\times(6\times10^{2}) = 4.2\times10^{6}$
  • $(6\times10^{4})\times(7\times10^{2}) = 4.2\times10^{7}$
  • $(42\times10^{8})\div(6\times10^{2}) = 7\times10^{6}$

• Multiplying and dividing by powers of ten.

  Hints

  When multiplying indices we add the powers if the base is the same.

  When dividing indices we subtract the powers if the base is the same.

  Solution

  • $10^{6}\times10^{2} = 10^{8}$
  • $10^{3}\times10^{4} = 10^{7}$
  • $10^{8}\div10^{2} = 10^{6}$
  • $10^{5}\div10^{2} = 10^{3}$

  When multiplying indices we add the powers if the base is the same.

  When dividing indices we subtract the powers if the base is the same.

• Divide the standard form numbers.

  Hints

  The operation we use for this problem is division.

  Distance from London to Sydney $\div$ Distance from London to Paris

  Distance from London to Sydney $\div$ Distance from London to Paris

  $(1.05\times10^{4})\div(2.9\times10^{2})$

  When we have divided $(1.05\times10^{4})\div(2.9\times10^{2})$ we need to make an adjustment to get the answer to the nearest whole number.

  Solution

  Answer is $36$