수와 연산 전체 문제

Multiply and Divide Using Scientific Notation

In the following exercises, multiply. Write your answer in decimal form.

$(3.5\,\times \,{10}^{-4})(1.6\,\times \,{10}^{-2})$

In the following exercises, divide. Write your answer in decimal form.

$\frac{7\,\times \,{10}^{-3}}{1\,\times \,{10}^{-7}}$

In the following exercises, divide. Write your answer in decimal form.

$\frac{5\,\times \,{10}^{-2}}{1\,\times \,{10}^{-10}}$

In the following exercises, divide. Write your answer in decimal form.

$\frac{6\,\times \,{10}^{4}}{3\,\times \,{10}^{-2}}$

In the following exercises, divide. Write your answer in decimal form.

$\frac{8\,\times \,{10}^{6}}{4\,\times \,{10}^{-1}}$

The average width of a human hair is 0.0018 centimeters. Write the number in scientific notation.

The probability of winning the 2010 Megamillions lottery was about 0.0000000057. Write the number in scientific notation.

In 2010, the number of Facebook users each day who changed their status to ‘engaged’ was $2\,\times \,{10}^{4}$. Convert this number to decimal form.

At the start of 2012, the US federal budget had a deficit of more than $\char36 1.5\,\times \,{10}^{13}$. Convert this number to decimal form.

The concentration of carbon dioxide in the atmosphere is $3.9\,\times \,{10}^{-4}$. Convert this number to decimal form.

The width of a proton is $1\,\times \,{10}^{-5}$ of the width of an atom. Convert this number to decimal form.

Health care costs The Centers for Medicare and Medicaid projects that consumers will spend more than $4 trillion on health care by 2017.

• ⓐ Write 4 trillion in decimal notation.
• ⓑ Write 4 trillion in scientific notation.

Coin production In 1942, the U.S. Mint produced 154,500,000 nickels. Write 154,500,000 in scientific notation.

Distance The distance between Earth and one of the brightest stars in the night star is 33.7 light years. One light year is about 6,000,000,000,000 (6 trillion), miles.

• ⓐ Write the number of miles in one light year in scientific notation.
• ⓑ Use scientific notation to find the distance between Earth and the star in miles. Write the answer in scientific notation.

• ⓐ Explain the meaning of the exponent in the expression ${2}^{3}$.
• ⓑ Explain the meaning of the exponent in the expression ${2}^{-3}$.

When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative?

Simplify: ⓐ ${9}^{2}$ ⓑ ${(-9)}^{2}$ ⓒ $-{9}^{2}$.

Round 3.846 to the nearest hundredth.

For each number, identify whether it is a real number or not a real number:

ⓐ $-\sqrt{100}$ ⓑ $\sqrt{-100}$.

Simplify: ⓐ $\sqrt{36}$ ⓑ $\sqrt{196}$ ⓒ $-\sqrt{81}$ ⓓ $-\sqrt{289}$.