Question

question 1 estimated number of dogs = 6.99 × 107=6.99 • 10,000,000=69,900,000estimated number of cats = 3.61 × 107=3.61 • 10,000,000= 36,100,000estimated number of birds = 8.3 × 106= 8.3 • 1,000,000= 8,300,000-------------------------------------------Question 2The estimated number of dogs is 6.99 x 10⁷The estimated number of cats is 3.61 x 10⁷The estimated number of birds is 8.3 x 10⁶The power of 10 in 8.3 x 10⁶ is 6 which is less than the power of 10 in the other two numbers. To make the calculation simpler, convert this number so the exponents are all the sameMultiply and divide 8.3 x 10⁶ by 10 to increase its exponent by 18.3x 10⁶= 10/10 • 8.3x 10⁶=8.3/10 •10⁶ •10= 0.83 x 10⁷

Answer 1

For question 1, we have

`\begin{gathered} 6.99*10^7=69,900,000 \\ 3.61*10^7=36,100,000 \\ 8.3*10^6=8,300,000 \end{gathered}`

Take the sum of the number above, we have

`\begin{gathered} 69,900,000+36,100,000+8,300,000 \\ =114,300,000 \end{gathered}`

For Question 2, we have

We need to add the number without converting to the ordinary form i.e will add the number in thier exponential form.

`6.99*10^7+3.61*10^7+0.83*10^7`

The exponent is the common factor, hence we add the other numbers

`\begin{gathered} (6.99+3.61+0.83)*10^7 \\ =11.43*10^7 \end{gathered}`

Changin the result in question 2 to ordinary form, we have

`11.43*10^7=11.43*10,000,000=114,300,000`

Hence

Yes the answer in question 1 and question 2 are the same.

We can tell this because the nunbers have the same values(they are the same) but are in different forms(ordinary form and the exponential form). Hence the numbers can be use interchangeably.