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?
- I understand what powers of ten are and how to work with them.
- I can express numbers in scientific notation.
- I know how to convert from scientific notation to standard form.
- I am familiar with rounding numbers to a specific decimal place.
- I can estimate populations and other large numbers using scientific notation.
- I can define key vocabulary related to scientific notation and exponents.
- I can work with both positive and negative exponents.
- I understand the concept of coefficients in scientific notation.
- I know different contexts in which scientific notation is used (e.g., astronomy, biology).
- 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!
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Round 8.266 to the nearest tenths.
- The tenths place is the first digit to the right of the decimal point: 8.26.
- Since 6 (the hundredths place) is more than 5, we round up.
- Answer: 8.3
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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
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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
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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
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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!