Exponent Application

Exponent Application

Unit 3​

By Kristin Harrell

Example #1​

Multiple Choice

When converting  $$0.\overline{78}$$  to a fraction, how many 9's should go in the denominator?

• 78

• 2

• 7

• 8

Multiple Choice

Convert  $$0.\overline{2}$$  to a fraction.

• $$\frac{2}{10}$$  

• $$\frac{2}{9}$$  

• $$\frac{2}{99}$$  

• $$\frac{1}{5}$$  

Multiple Choice

Convert  $$0.\overline{24545}$$  to a fraction.

• $$\frac{24545}{99999}$$  

• $$\frac{24545}{99}$$  

• $$2\frac{45}{99}$$  

• $$\frac{24545}{100,000}$$  

Multiple Choice

• 1/2
• 1/10
• 1/100
• 1/9

Multiple Choice

• 7/50
• 14/9
• 7/45
• 14/99

Multiple Choice

• 77/25
• 77/250
• 308/9
• 308/999

Multiple Choice

Identify the fraction equivalent to the decimal below.

• 2 4/99
• 2   4/9
• 2   2/5
• 2 4/10

Multiple Choice

Change from standard form to scientific notation: 12,000,000

• 12.0  x  10⁷
• 0.12  x  10⁷
• 1.2  x  10⁶
• 1.2  x  10⁷

Multiple Choice

Change from standard form to scientific notation:  450,000

• 4.5  x  10⁵
• 45  x  10⁵
• 4.5  x  10⁴
• 4.5  x  10⁶

Multiple Choice

Change from standard form to scientific notation: 0.004078

• 4.078  x  10^-3
• 4.078  x  10³
• 40.78  x  10^-4
• .4078  x  10^-2

Multiple Choice

125,678,000: Change to scientific notation

• 1.25678  x  10¹²
• .125678  x  10^-9
• 12.5678  x  10⁸
• 1.25678  x  10⁸

Multiple Choice

Try to change the number back to standard form:  6.79  x  10⁴

• 679,000
• 6,790
• 67,900
• 6,790,000

Multiple Choice

Try to change the number back to standard form: 3.97  x  10^-2

• 0.000397
• 0.0397
• 0.0000397
• 0.397

Multiple Choice

How would you write 564,000,000 in scientific notation?

• 5.64 x 10^-7
• 5.64 x 10⁶
• 5.64 x 10⁸
• 56.4 x 10⁷

Multiple Choice

When writing a number in scientific notation, the first number must be greater than 1, but less than 10.

• False
• True

Multiple Choice

Express the following in scientific notation:
.000457

• 457 x 10⁶
• 457 x 10^-6
• 4.57 x10⁴
• 4.57 x 10^-4

Multiple Choice

Which of the following is correct scientific notation?

• 20.35 x 10⁴
• .2035 x 10⁴
• 2035 ⁴
• 2.035 x10⁴

Multiplying in scientific notation:

-multiply the leading numbers

-add the exponents

​

Dividing in scientific notation:

-divide the leading numbers

-subtract the exponents

​

Multiple Choice

Multiply:

$$\left(6\times10^3\right)\times\left(2\times10^{10}\right)$$  

• $$\left(6\times2\right)\times10^{\left(3+10\right)}$$  

• $$\left(6+2\right)\times10^{\left(3+10\right)}$$  

• $$\left(6\times2\right)\times10^{\left(3\times10\right)}$$  

• $$\left(6+2\right)\times10^{\left(3\times10\right)}$$  

Multiple Choice

Multiply:

$$\left(4\times10^5\right)\times\left(6\times10^1\right)$$  

• $$\left(4\times6\right)\times10^{\left(5\times1\right)}$$  

• $$\left(4\times6\right)\times10^{\left(5+1\right)}$$  

Multiple Choice

Divide: $$\left(6\times10^{10}\right)\div\left(2\times10^3\right)$$  

• $$\left(6\div2\right)\times10^{\left(10-3\right)}$$  

• $$\left(6\div2\right)\times10^{\left(10\div3\right)}$$  

Multiple Choice

Divide: $$\left(12\times10^6\right)\div\left(4\times10^2\right)$$  

• $$\left(12-4\right)\times10^{\left(6-2\right)}$$  

• $$\left(12\div4\right)\times10^{\left(6-2\right)}$$  

When adding or subtracting numbers in scientific notation, the exponents must be the same.

• Step 1 - add/subtract the decimal

• Step 2 – Bring down the given exponent on the 10

When adding or subtracting numbers in scientific notation, the exponents must be the same.

• Step 1 - add/subtract the decimal

• Step 2 – Bring down the given exponent on the 10

Multiple Choice

$$\left(5.6×10^8\right)−\left(3.24×10^8\right)$$  

• $$8.84\times10^8$$  

• $$2.44\times10^8$$  

• $$2.36\times10^8$$  

Multiple Choice

$$\left(1.95×10^{12}\right)+\left(8.02×10^{12}\right)$$  

• $$9.97\times10^{12}$$  

• $$7.93\times10^{12}$$  

• $$6.07\times10^{12}$$  

Adding/Subtracting when the Exponents are DIFFERENT

• Step 1 – Rewrite so the exponents are the same 

• Step 2 - add/subtract the decimal

• Step 3 – Bring down the given exponent on the 10

Multiple Choice

$$(4.23×10^3)–(9.56×10^2)$$  

• $$32.74×10^2$$  

• $$3.274×10^3$$  

• $$3.274×10^2$$  

Multiple Choice

$$\left(7.6×10^{-15}\right)−\left(4.91×10^{-16}\right)$$  

• $$7.109\times10^{-15}$$  

• $$7.109\times10^{-16}$$  

• $$7109\times10^{-15}$$  

Multiple Choice

$$\left(2.7×10^{10}\right)+\left(4.71×10^9\right)$$  

• $$31.71\times10^9$$  

• $$3.171\times10^9$$  

• $$3.171\times10^{10}$$  

Rational

Values that can be written as a fraction.

Look for: fractions, whole numbers, terminating decimals, repeating decimals, and perfect squares.

Irrational

Values that can NOT be written as a fraction.

Look for: Never-ending non-repeating decimals, pi, and imperfect squares.

Multiple Choice

Categorize the following:  $$\frac{3}{4}$$   

• Rational

• Irrational

Multiple Choice

Categorize the following:  $$-32$$  

• Rational

• Irrational

Multiple Choice

Categorize the following:  $$5.984732...$$  

• Rational

• Irrational

Multiple Choice

Categorize the following:  $$7.\overline{5}$$  

• Rational

• Irrational

Multiple Choice

Categorize the following:  $$-2.3$$  

• Rational

• Irrational

Multiple Choice

Categorize the following: $$\sqrt{36}$$  

• Rational

• Irrational

Multiple Choice

Categorize the following: $$\sqrt{15}$$  

• Rational

• Irrational

Multiple Choice

What kind of number is   π   ?

• rational
• irrational

Multiple Choice

Is 3.74 a rational number?

• yes
• no

Multiple Choice

Is -5/8 a rational number?

• yes
• no

Multiple Choice

A REPEATING decimal is what type of number?

• Rational 
• Irrational

Multiple Choice

The square root of 2 is an irrational number because...

• All square roots are irrational
• The answer is a decimal that never stops
• Two is an even number
• The answer is 1

Multiple Choice

-17.5

• Rational 
• Irrational