Question
Vocabulary Terms - Define/Illustrate
Percent Increase or Decrease
Finish this statement - Scientific Notation is useful for _________________.
Problems - SHOW ALL WORK!
1. In 2013 the Los Angeles Dodgers opening day payroll was about $2.16 x 10^8 and the Houston Astros opening day payroll was about $2.4 x 10^7.
How much higher was the Dodgers’ payroll?
How many times higher is the Dodgers payroll?
2. A TV show had 3.5 x 10^6 viewers for their first episode and 8.5 x 10^6 viewers for their second episode.
How many viewers did they have overall?
3. A dime is approximately 1.35 x 10^-1cm thick. The thickness of a dollar bill is approximately 1.2 x 10^-2
How many times greater is the thickness of a dime than the thickness of a dollar bill?
4. A corporation earned a profit of $2.5 x 10^4 for 1 x 10^3 days in a row.
What was the corporation’s total profit during this time period?
Percent Increase or Decrease
Finish this statement - Scientific Notation is useful for _________________.
Problems - SHOW ALL WORK!
1. In 2013 the Los Angeles Dodgers opening day payroll was about $2.16 x 10^8 and the Houston Astros opening day payroll was about $2.4 x 10^7.
How much higher was the Dodgers’ payroll?
How many times higher is the Dodgers payroll?
2. A TV show had 3.5 x 10^6 viewers for their first episode and 8.5 x 10^6 viewers for their second episode.
How many viewers did they have overall?
3. A dime is approximately 1.35 x 10^-1cm thick. The thickness of a dollar bill is approximately 1.2 x 10^-2
How many times greater is the thickness of a dime than the thickness of a dollar bill?
4. A corporation earned a profit of $2.5 x 10^4 for 1 x 10^3 days in a row.
What was the corporation’s total profit during this time period?
Answers
Answered by
GPT-4o mini
### Vocabulary Terms
**Percent Increase or Decrease**: Percent increase refers to the amount that an original value grows, expressed as a percentage of that original value. Percent decrease refers to the amount that an original value shrinks, also expressed as a percentage of that original value.
**Finish this statement**: Scientific Notation is useful for expressing very large or very small numbers in a compact form that makes calculations and comparisons easier.
### Problems - SHOW ALL WORK!
**1. In 2013 the Los Angeles Dodgers opening day payroll was about \(2.16 \times 10^8\) and the Houston Astros opening day payroll was about \(2.4 \times 10^7\).**
**How much higher was the Dodgers’ payroll?**
To find how much higher the Dodgers’ payroll was, we subtract the Astros' payroll from the Dodgers' payroll:
\[
\text{Difference} = (2.16 \times 10^8) - (2.4 \times 10^7)
\]
First, convert \(2.4 \times 10^7\) to have the same exponent as \(2.16 \times 10^8\):
\[
2.4 \times 10^7 = 0.24 \times 10^8
\]
Now, substitute back into the equation:
\[
\text{Difference} = (2.16 \times 10^8) - (0.24 \times 10^8) = (2.16 - 0.24) \times 10^8 = 1.92 \times 10^8
\]
So, the Dodgers’ payroll was \(1.92 \times 10^8\) higher than the Astros' payroll.
**How many times higher is the Dodgers' payroll?**
To find how many times higher the Dodgers’ payroll is than the Astros' payroll, we divide the Dodgers' payroll by the Astros' payroll:
\[
\text{Times higher} = \frac{Dodgers' \; payroll}{Astros' \; payroll} = \frac{2.16 \times 10^8}{2.4 \times 10^7}
\]
Convert both to have a common exponent:
\[
= \frac{2.16 \times 10^8}{0.24 \times 10^8} = \frac{2.16}{0.24} = 9
\]
So, the Dodgers' payroll is 9 times higher than the Astros' payroll.
---
**2. A TV show had \(3.5 \times 10^6\) viewers for their first episode and \(8.5 \times 10^6\) viewers for their second episode.**
**How many viewers did they have overall?**
To find the total viewers,
\[
\text{Total viewers} = (3.5 \times 10^6) + (8.5 \times 10^6)
\]
Since both have the same exponent, add the coefficients:
\[
= (3.5 + 8.5) \times 10^6 = 12 \times 10^6 = 1.2 \times 10^7
\]
So, the TV show had \(1.2 \times 10^7\) viewers overall.
---
**3. A dime is approximately \(1.35 \times 10^{-1}\)cm thick. The thickness of a dollar bill is approximately \(1.2 \times 10^{-2}\) cm.**
**How many times greater is the thickness of a dime than the thickness of a dollar bill?**
To determine how many times greater the dime’s thickness is than the dollar bill’s thickness, we calculate:
\[
\text{Times greater} = \frac{\text{Thickness of dime}}{\text{Thickness of dollar bill}} = \frac{1.35 \times 10^{-1}}{1.2 \times 10^{-2}}
\]
Divide the coefficients:
\[
= \frac{1.35}{1.2} \times \frac{10^{-1}}{10^{-2}} = 1.125 \times 10^{1} = 11.25
\]
So, the thickness of a dime is \(11.25\) times greater than the thickness of a dollar bill.
---
**4. A corporation earned a profit of \(2.5 \times 10^4\) for \(1 \times 10^3\) days in a row.**
**What was the corporation’s total profit during this time period?**
To find the total profit, multiply the daily profit by the number of days:
\[
\text{Total profit} = (2.5 \times 10^4) \times (1 \times 10^3)
\]
Multiply the coefficients and add the exponents:
\[
= 2.5 \times 1 \times 10^{4+3} = 2.5 \times 10^7
\]
So, the corporation's total profit during this time period was \(2.5 \times 10^7\).
**Percent Increase or Decrease**: Percent increase refers to the amount that an original value grows, expressed as a percentage of that original value. Percent decrease refers to the amount that an original value shrinks, also expressed as a percentage of that original value.
**Finish this statement**: Scientific Notation is useful for expressing very large or very small numbers in a compact form that makes calculations and comparisons easier.
### Problems - SHOW ALL WORK!
**1. In 2013 the Los Angeles Dodgers opening day payroll was about \(2.16 \times 10^8\) and the Houston Astros opening day payroll was about \(2.4 \times 10^7\).**
**How much higher was the Dodgers’ payroll?**
To find how much higher the Dodgers’ payroll was, we subtract the Astros' payroll from the Dodgers' payroll:
\[
\text{Difference} = (2.16 \times 10^8) - (2.4 \times 10^7)
\]
First, convert \(2.4 \times 10^7\) to have the same exponent as \(2.16 \times 10^8\):
\[
2.4 \times 10^7 = 0.24 \times 10^8
\]
Now, substitute back into the equation:
\[
\text{Difference} = (2.16 \times 10^8) - (0.24 \times 10^8) = (2.16 - 0.24) \times 10^8 = 1.92 \times 10^8
\]
So, the Dodgers’ payroll was \(1.92 \times 10^8\) higher than the Astros' payroll.
**How many times higher is the Dodgers' payroll?**
To find how many times higher the Dodgers’ payroll is than the Astros' payroll, we divide the Dodgers' payroll by the Astros' payroll:
\[
\text{Times higher} = \frac{Dodgers' \; payroll}{Astros' \; payroll} = \frac{2.16 \times 10^8}{2.4 \times 10^7}
\]
Convert both to have a common exponent:
\[
= \frac{2.16 \times 10^8}{0.24 \times 10^8} = \frac{2.16}{0.24} = 9
\]
So, the Dodgers' payroll is 9 times higher than the Astros' payroll.
---
**2. A TV show had \(3.5 \times 10^6\) viewers for their first episode and \(8.5 \times 10^6\) viewers for their second episode.**
**How many viewers did they have overall?**
To find the total viewers,
\[
\text{Total viewers} = (3.5 \times 10^6) + (8.5 \times 10^6)
\]
Since both have the same exponent, add the coefficients:
\[
= (3.5 + 8.5) \times 10^6 = 12 \times 10^6 = 1.2 \times 10^7
\]
So, the TV show had \(1.2 \times 10^7\) viewers overall.
---
**3. A dime is approximately \(1.35 \times 10^{-1}\)cm thick. The thickness of a dollar bill is approximately \(1.2 \times 10^{-2}\) cm.**
**How many times greater is the thickness of a dime than the thickness of a dollar bill?**
To determine how many times greater the dime’s thickness is than the dollar bill’s thickness, we calculate:
\[
\text{Times greater} = \frac{\text{Thickness of dime}}{\text{Thickness of dollar bill}} = \frac{1.35 \times 10^{-1}}{1.2 \times 10^{-2}}
\]
Divide the coefficients:
\[
= \frac{1.35}{1.2} \times \frac{10^{-1}}{10^{-2}} = 1.125 \times 10^{1} = 11.25
\]
So, the thickness of a dime is \(11.25\) times greater than the thickness of a dollar bill.
---
**4. A corporation earned a profit of \(2.5 \times 10^4\) for \(1 \times 10^3\) days in a row.**
**What was the corporation’s total profit during this time period?**
To find the total profit, multiply the daily profit by the number of days:
\[
\text{Total profit} = (2.5 \times 10^4) \times (1 \times 10^3)
\]
Multiply the coefficients and add the exponents:
\[
= 2.5 \times 1 \times 10^{4+3} = 2.5 \times 10^7
\]
So, the corporation's total profit during this time period was \(2.5 \times 10^7\).
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