Question
Math Practice U4-L1
Unit 4 Math Practice Links - Click Here
Live Lesson Recording
*Passcode can be found on the Connexus Pushpin under your Math Class! Use the one for Mrs. Garcia!
Function of the Day: Expression --------------- Value
Expression: 10^-3, 10^6, 10^9, 10^-2, 10^12, 10^3
Value: 1,000,000,000,000, 1/100, 1,000, 1,000,000,000, 1,000,000, 1/1000
What do you know?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Vocabulary Terms - Define/Illustrate
Scientific Notation
Our number system is based on _________ ?
Coefficient
5 Problems - SHOW ALL WORK!
Round 8.266 to the nearest tenths.
Write in standard form:
The distance from Earth to Jupiter is 553.26 million miles.
Write in standard form:
A red blood cell’s diameter is about 7 millionths of a meter.
Los Angeles has a population of 3,971,883 people. Estimate the population as a single digit number times a power of 10.
Write 100,000 in exponential notation with a base of 10.
What do I need help with?
Unit 4 Math Practice Links - Click Here
Live Lesson Recording
*Passcode can be found on the Connexus Pushpin under your Math Class! Use the one for Mrs. Garcia!
Function of the Day: Expression --------------- Value
Expression: 10^-3, 10^6, 10^9, 10^-2, 10^12, 10^3
Value: 1,000,000,000,000, 1/100, 1,000, 1,000,000,000, 1,000,000, 1/1000
What do you know?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Vocabulary Terms - Define/Illustrate
Scientific Notation
Our number system is based on _________ ?
Coefficient
5 Problems - SHOW ALL WORK!
Round 8.266 to the nearest tenths.
Write in standard form:
The distance from Earth to Jupiter is 553.26 million miles.
Write in standard form:
A red blood cell’s diameter is about 7 millionths of a meter.
Los Angeles has a population of 3,971,883 people. Estimate the population as a single digit number times a power of 10.
Write 100,000 in exponential notation with a base of 10.
What do I need help with?
Answers
GPT-4o mini
It looks like you're working on a math practice related to scientific notation, exponential notation, and rounding. Here's how you can tackle the different sections noted above:
### What do you know?
1. I understand what powers of ten are and how to work with them.
2. I can express numbers in scientific notation.
3. I know how to convert from scientific notation to standard form.
4. I am familiar with rounding numbers to a specific decimal place.
5. I can estimate populations and other large numbers using scientific notation.
6. I can define key vocabulary related to scientific notation and exponents.
7. I can work with both positive and negative exponents.
8. I understand the concept of coefficients in scientific notation.
9. I know different contexts in which scientific notation is used (e.g., astronomy, biology).
10. I can apply math concepts to real-world problems.
### Vocabulary Terms - Define/Illustrate
**Scientific Notation**: A way to express very large or very small numbers by using powers of ten. It is written in the form \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer.
**Our number system is based on**: The base 10 system, also known as the decimal system.
**Coefficient**: In scientific notation, the coefficient is the number \( a \) in the expression \( a \times 10^n \).
### 5 Problems - SHOW ALL WORK!
1. **Round 8.266 to the nearest tenths.**
- The tenths place is the first digit to the right of the decimal point: 8.2**6**.
- Since 6 (the hundredths place) is more than 5, we round up.
- Answer: **8.3**
2. **Write in standard form: The distance from Earth to Jupiter is 553.26 million miles.**
- First, convert million to standard notation: 1 million = \( 10^6 \).
- Therefore, 553.26 million = \( 553.26 \times 10^6 \) miles.
- Answer: **553,260,000 miles** or **5.5326 × 10^8 miles**
3. **Write in standard form: A red blood cell’s diameter is about 7 millionths of a meter.**
- Convert millionths to standard form: 1 millionth = \( 10^{-6} \).
- Therefore, 7 millionths = \( 7 \times 10^{-6} \) meters.
- Answer: **7 × 10^-6 meters**
4. **Los Angeles has a population of 3,971,883 people. Estimate the population as a single digit number times a power of 10.**
- Round 3,971,883 to the nearest significant figure: approximately 4 million.
- In scientific notation, this is \( 4 \times 10^6 \).
- Answer: **4 × 10^6**
5. **Write 100,000 in exponential notation with a base of 10.**
- 100,000 can be expressed as \( 10^5 \) because \( 10^5 = 100,000 \).
- Answer: **10^5**
### What do I need help with?
- If you have specific areas or problems you’re struggling with, it would be helpful to specify those so I can help you more effectively! Are you having trouble with concepts in scientific notation, rounding, or anything else? Let me know!
### What do you know?
1. I understand what powers of ten are and how to work with them.
2. I can express numbers in scientific notation.
3. I know how to convert from scientific notation to standard form.
4. I am familiar with rounding numbers to a specific decimal place.
5. I can estimate populations and other large numbers using scientific notation.
6. I can define key vocabulary related to scientific notation and exponents.
7. I can work with both positive and negative exponents.
8. I understand the concept of coefficients in scientific notation.
9. I know different contexts in which scientific notation is used (e.g., astronomy, biology).
10. I can apply math concepts to real-world problems.
### Vocabulary Terms - Define/Illustrate
**Scientific Notation**: A way to express very large or very small numbers by using powers of ten. It is written in the form \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer.
**Our number system is based on**: The base 10 system, also known as the decimal system.
**Coefficient**: In scientific notation, the coefficient is the number \( a \) in the expression \( a \times 10^n \).
### 5 Problems - SHOW ALL WORK!
1. **Round 8.266 to the nearest tenths.**
- The tenths place is the first digit to the right of the decimal point: 8.2**6**.
- Since 6 (the hundredths place) is more than 5, we round up.
- Answer: **8.3**
2. **Write in standard form: The distance from Earth to Jupiter is 553.26 million miles.**
- First, convert million to standard notation: 1 million = \( 10^6 \).
- Therefore, 553.26 million = \( 553.26 \times 10^6 \) miles.
- Answer: **553,260,000 miles** or **5.5326 × 10^8 miles**
3. **Write in standard form: A red blood cell’s diameter is about 7 millionths of a meter.**
- Convert millionths to standard form: 1 millionth = \( 10^{-6} \).
- Therefore, 7 millionths = \( 7 \times 10^{-6} \) meters.
- Answer: **7 × 10^-6 meters**
4. **Los Angeles has a population of 3,971,883 people. Estimate the population as a single digit number times a power of 10.**
- Round 3,971,883 to the nearest significant figure: approximately 4 million.
- In scientific notation, this is \( 4 \times 10^6 \).
- Answer: **4 × 10^6**
5. **Write 100,000 in exponential notation with a base of 10.**
- 100,000 can be expressed as \( 10^5 \) because \( 10^5 = 100,000 \).
- Answer: **10^5**
### What do I need help with?
- If you have specific areas or problems you’re struggling with, it would be helpful to specify those so I can help you more effectively! Are you having trouble with concepts in scientific notation, rounding, or anything else? Let me know!