Question
Vocabulary Terms - Define/Illustrate
Inference vs. Estimate
Integer power of 10 meaning?
5 Problems - SHOW ALL WORK!
Which is larger? How do you know?
2.75 x 10^3 or 4.92 x 10^2 ?
The moon is 238,900 miles from the Earth.
Estimate the distance as the product of a single digit number times an integer power of 10.
Write the number 0.0000000678 as the product of a single digit number times an integer power of 10.
Write the number 0.0000000000276 as the product of a single number times an integer power of 10.
Make a table of the powers of 10 from 10^5 to 10^-5 using the pattern to show negative powers.
10^5
100,000
10^4
10^3
10^2
10^1
10^0
10^-1
10^-2
10^-3
10^-4
10^-5
Inference vs. Estimate
Integer power of 10 meaning?
5 Problems - SHOW ALL WORK!
Which is larger? How do you know?
2.75 x 10^3 or 4.92 x 10^2 ?
The moon is 238,900 miles from the Earth.
Estimate the distance as the product of a single digit number times an integer power of 10.
Write the number 0.0000000678 as the product of a single digit number times an integer power of 10.
Write the number 0.0000000000276 as the product of a single number times an integer power of 10.
Make a table of the powers of 10 from 10^5 to 10^-5 using the pattern to show negative powers.
10^5
100,000
10^4
10^3
10^2
10^1
10^0
10^-1
10^-2
10^-3
10^-4
10^-5
Answers
Answered by
GPT-4o mini
### Vocabulary Terms
1. **Inference**: An inference is a conclusion or judgment that is formed based on evidence or reasoning. It refers to the act of drawing a logical conclusion from premises known or assumed to be true. For example, if you see wet streets, you might infer that it rained.
2. **Estimate**: An estimate is an approximate calculation or judgment regarding the value, number, quantity, or extent of something. Estimations are often used in situations where a precise answer is difficult to obtain. For example, if you are asked to estimate how many jellybeans are in a jar, you might count a small section and multiply by the total number of sections.
3. **Integer Power of 10**: An integer power of 10 means any whole number as an exponent of 10. For example, \(10^3\) means \(10 \times 10 \times 10 = 1000\). Negative powers, like \(10^{-2}\), indicate division by that power of ten, such as \(10^{-2} = \frac{1}{10^2} = 0.01\).
### 5 Problems with Work Shown
#### Problem 1: Compare \(2.75 \times 10^3\) and \(4.92 \times 10^2\)
1. Convert both to standard form:
- \(2.75 \times 10^3 = 2.75 \times 1000 = 2750\)
- \(4.92 \times 10^2 = 4.92 \times 100 = 492\)
2. Compare the two numbers:
- \(2750 > 492\)
**Conclusion**: \(2.75 \times 10^3\) is larger than \(4.92 \times 10^2\).
---
#### Problem 2: Estimate the distance to the Moon
The distance to the Moon is \(238,900\) miles. To express this as a product of a single digit number and a power of 10:
1. Identify a single-digit number close to \(238,900\):
- The closest single-digit number is \(2\).
2. Rewrite \(238,900\):
- \(238,900 \approx 2.389 \times 10^5\) (or we can round it to \(2.4\), thus become \(2.4 \times 10^5\)).
**Estimation**: \(2.4 \times 10^5\) miles.
---
#### Problem 3: Write \(0.0000000678\) as a product
1. Move the decimal point to the right until we reach a single-digit number:
- \(0.0000000678\) becomes \(6.78\) (after moving it 8 places).
2. Since we moved the decimal, we apply a negative exponent:
- Thus, \(0.0000000678 = 6.78 \times 10^{-9}\).
---
#### Problem 4: Write \(0.0000000000276\) as a product
1. Move the decimal point to the right until we reach a single-digit number:
- \(0.0000000000276\) becomes \(2.76\) (after moving it 11 places).
2. This gives us:
- \(0.0000000000276 = 2.76 \times 10^{-11}\).
---
#### Problem 5: Table of Powers of 10 from \(10^5\) to \(10^{-5}\)
| Power | Value |
|----------|-------------|
| \(10^5\) | 100,000 |
| \(10^4\) | 10,000 |
| \(10^3\) | 1,000 |
| \(10^2\) | 100 |
| \(10^1\) | 10 |
| \(10^0\) | 1 |
| \(10^{-1}\) | 0.1 |
| \(10^{-2}\) | 0.01 |
| \(10^{-3}\) | 0.001 |
| \(10^{-4}\) | 0.0001 |
| \(10^{-5}\) | 0.00001 |
This table shows not only positive powers of 10 but also the corresponding negative powers down to \(10^{-5}\).
1. **Inference**: An inference is a conclusion or judgment that is formed based on evidence or reasoning. It refers to the act of drawing a logical conclusion from premises known or assumed to be true. For example, if you see wet streets, you might infer that it rained.
2. **Estimate**: An estimate is an approximate calculation or judgment regarding the value, number, quantity, or extent of something. Estimations are often used in situations where a precise answer is difficult to obtain. For example, if you are asked to estimate how many jellybeans are in a jar, you might count a small section and multiply by the total number of sections.
3. **Integer Power of 10**: An integer power of 10 means any whole number as an exponent of 10. For example, \(10^3\) means \(10 \times 10 \times 10 = 1000\). Negative powers, like \(10^{-2}\), indicate division by that power of ten, such as \(10^{-2} = \frac{1}{10^2} = 0.01\).
### 5 Problems with Work Shown
#### Problem 1: Compare \(2.75 \times 10^3\) and \(4.92 \times 10^2\)
1. Convert both to standard form:
- \(2.75 \times 10^3 = 2.75 \times 1000 = 2750\)
- \(4.92 \times 10^2 = 4.92 \times 100 = 492\)
2. Compare the two numbers:
- \(2750 > 492\)
**Conclusion**: \(2.75 \times 10^3\) is larger than \(4.92 \times 10^2\).
---
#### Problem 2: Estimate the distance to the Moon
The distance to the Moon is \(238,900\) miles. To express this as a product of a single digit number and a power of 10:
1. Identify a single-digit number close to \(238,900\):
- The closest single-digit number is \(2\).
2. Rewrite \(238,900\):
- \(238,900 \approx 2.389 \times 10^5\) (or we can round it to \(2.4\), thus become \(2.4 \times 10^5\)).
**Estimation**: \(2.4 \times 10^5\) miles.
---
#### Problem 3: Write \(0.0000000678\) as a product
1. Move the decimal point to the right until we reach a single-digit number:
- \(0.0000000678\) becomes \(6.78\) (after moving it 8 places).
2. Since we moved the decimal, we apply a negative exponent:
- Thus, \(0.0000000678 = 6.78 \times 10^{-9}\).
---
#### Problem 4: Write \(0.0000000000276\) as a product
1. Move the decimal point to the right until we reach a single-digit number:
- \(0.0000000000276\) becomes \(2.76\) (after moving it 11 places).
2. This gives us:
- \(0.0000000000276 = 2.76 \times 10^{-11}\).
---
#### Problem 5: Table of Powers of 10 from \(10^5\) to \(10^{-5}\)
| Power | Value |
|----------|-------------|
| \(10^5\) | 100,000 |
| \(10^4\) | 10,000 |
| \(10^3\) | 1,000 |
| \(10^2\) | 100 |
| \(10^1\) | 10 |
| \(10^0\) | 1 |
| \(10^{-1}\) | 0.1 |
| \(10^{-2}\) | 0.01 |
| \(10^{-3}\) | 0.001 |
| \(10^{-4}\) | 0.0001 |
| \(10^{-5}\) | 0.00001 |
This table shows not only positive powers of 10 but also the corresponding negative powers down to \(10^{-5}\).
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