Question

Mary simplified an expression and got 12.9x10^4 for her answer in scientific notation. Her friend, Angela, is telling her that her answer is incorrect. Why is Angela telling her she is incorrect? What is the correct way to write that number in scientific notation?

Answer 1

Answer:

Mary simplified an expression. $1.29 \times 10^{5}$ is correct representation in scientific notation.

Solution:

Given that Mary simplified an expression and got $12.9 \times 10^{4}$ for answer in scientific notation.

According to Angela, answer is incorrect. Need to find reason why Angela consider $12.9 \times 10^{4}$ as incorrect scientific notation and find the correct answer.

Let’s understand what is scientific notation of any number.

Scientific notation is a way of representing number between 1 and 10 including 1 and excluding 10 multiplied by appropriate power of 10.

According to Mary’s simplification the number she is getting is 12.9 but in scientific notation, number must be in between 1 to 10

So $12.9 \times 10^{4}$ is not correct scientific notation.

$\text { Let's rewrite } 12.9 \times 10^{4} \text { as } 1.29 \times 10^{1} \times 10^{4}=1.29 \times 10^{5}$

Now we got 1.29 which is in between 1 and 10 multiplied by $10^5$

Hence $1.29 \times 10^{5}$ is correct representation in scientific notation.