Question
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.
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.
Answers
Answered by
GPT-4o mini
### Vocabulary Terms
**Scientific Notation**: A way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is represented as \( a \times 10^n \), where \( a \) is a coefficient (a number between 1 and 10), and \( n \) is an integer.
**Our number system is based on**: 10 (the decimal system).
**Coefficient**: In scientific notation, the coefficient is the number \( a \) in the expression \( a \times 10^n \), and it typically lies between 1 and 10.
---
### 5 Problems - SHOW ALL WORK!
1. **Round 8.266 to the nearest tenths**:
- Look at the hundredths place (the second digit after the decimal point): 8.266 → The hundredths digit is 6.
- Since 6 is 5 or greater, we round up the tenths place (which is 2).
- Therefore, \( 8.266 \) rounded to the nearest tenths is \( 8.3 \).
**Final Answer**: **8.3**
2. **Write in standard form: The distance from Earth to Jupiter is 553.26 million miles**:
- First, convert million miles to standard form: \( 553.26 \) million can be represented as \( 553.26 \times 10^6 \) miles.
- Now, to express it in standard scientific notation.
- Move the decimal point in \( 553.26 \) two places to the left to get \( 5.5326 \) and adjust the exponent accordingly (increase by 2):
\[
553.26 \times 10^6 = 5.5326 \times 10^8
\]
**Final Answer**: **\( 5.5326 \times 10^8 \) miles**
3. **Write in standard form: A red blood cell’s diameter is about 7 millionths of a meter**:
- Express millionths in standard form: \( 7 \) millionths is \( 7 \times 10^{-6} \) meters.
**Final Answer**: **\( 7 \times 10^{-6} \) 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**:
- We can round \( 3,971,883 \) to \( 4,000,000 \) for estimation.
- This can be expressed as \( 4 \times 10^6 \).
**Final Answer**: **\( 4 \times 10^6 \) people**
5. **Write 100,000 in exponential notation with a base of 10**:
- Express \( 100,000 \) as a power of 10:
\[
100,000 = 10^5
\]
**Final Answer**: **\( 10^5 \)**
**Scientific Notation**: A way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is represented as \( a \times 10^n \), where \( a \) is a coefficient (a number between 1 and 10), and \( n \) is an integer.
**Our number system is based on**: 10 (the decimal system).
**Coefficient**: In scientific notation, the coefficient is the number \( a \) in the expression \( a \times 10^n \), and it typically lies between 1 and 10.
---
### 5 Problems - SHOW ALL WORK!
1. **Round 8.266 to the nearest tenths**:
- Look at the hundredths place (the second digit after the decimal point): 8.266 → The hundredths digit is 6.
- Since 6 is 5 or greater, we round up the tenths place (which is 2).
- Therefore, \( 8.266 \) rounded to the nearest tenths is \( 8.3 \).
**Final Answer**: **8.3**
2. **Write in standard form: The distance from Earth to Jupiter is 553.26 million miles**:
- First, convert million miles to standard form: \( 553.26 \) million can be represented as \( 553.26 \times 10^6 \) miles.
- Now, to express it in standard scientific notation.
- Move the decimal point in \( 553.26 \) two places to the left to get \( 5.5326 \) and adjust the exponent accordingly (increase by 2):
\[
553.26 \times 10^6 = 5.5326 \times 10^8
\]
**Final Answer**: **\( 5.5326 \times 10^8 \) miles**
3. **Write in standard form: A red blood cell’s diameter is about 7 millionths of a meter**:
- Express millionths in standard form: \( 7 \) millionths is \( 7 \times 10^{-6} \) meters.
**Final Answer**: **\( 7 \times 10^{-6} \) 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**:
- We can round \( 3,971,883 \) to \( 4,000,000 \) for estimation.
- This can be expressed as \( 4 \times 10^6 \).
**Final Answer**: **\( 4 \times 10^6 \) people**
5. **Write 100,000 in exponential notation with a base of 10**:
- Express \( 100,000 \) as a power of 10:
\[
100,000 = 10^5
\]
**Final Answer**: **\( 10^5 \)**
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