Question

3 multiple choice 2 points what is 9.01×10^5 in standard form? 901,000 90,100 90,100,000 901,000,000 4 multiple choice 2 points which represents a rational number? √16 √(100/5) √15 π 5 multiple choice 2 points when the number 0.00716 is written in the form 7.16×10^x, what is the value of x? 3 -2 -1 -3

Explanation:

Question 3

Step1: Recall scientific - notation rule

The scientific notation $a\times10^{n}$ where $1\leq a<10$ and $n$ is an integer. To convert $9.01\times 10^{5}$ to standard form, we move the decimal point $n$ places to the right when $n>0$.

Step2: Move the decimal point

Since $n = 5$, we move the decimal point in $9.01$ five places to the right. So $9.01\times10^{5}=901000$.

Step1: Recall the definition of rational numbers

A rational number is a number that can be written as $\frac{p}{q}$ where $p$ and $q$ are integers and $q
eq0$. Also, a perfect - square's square root is rational.

Step2: Analyze each option

• $\sqrt{16}=4$, which is rational since $4=\frac{4}{1}$.
• $\sqrt{\frac{100}{5}}=\sqrt{20}=2\sqrt{5}$, which is irrational.
• $\sqrt{15}$ is irrational because 15 is not a perfect square.
• $\pi$ is an irrational number.

Step1: Recall scientific - notation rule

The scientific notation is $a\times 10^{n}$, where $1\leq a<10$. To convert a number to scientific notation, we move the decimal point. If we start with $0.00716$ and rewrite it as $7.16\times 10^{x}$, we moved the decimal point 3 places to the right. When we move the decimal point to the right, the exponent of 10 is negative.

Step2: Determine the exponent

Since we moved the decimal point 3 places to the right, $x=-3$.

Answer:

A. 901,000

Question 4