Answer :
Sure! Let's break down each part of the question step-by-step.
### 10.1 Write the following in scientific notation
#### 10.1.15 5133000000000
To convert 5133000000000 into scientific notation:
1. Place the decimal after the first non-zero digit: 5.133.
2. Count the number of places you moved the decimal. In this case, it's 12 places to the right.
3. Write the result as: [tex]\(5.133 \times 10^{12}\)[/tex].
#### 10.1.2. 0.0000006523
To convert 0.0000006523 into scientific notation:
1. Place the decimal after the first non-zero digit: 6.523.
2. Count the number of places you moved the decimal. Here, it is 7 places to the left.
3. Write the result as: [tex]\(6.523 \times 10^{-7}\)[/tex].
### 10.2 Write the following in expanded form
#### 10.2.1 [tex]\(3.22 \times 10^4\)[/tex]
To convert [tex]\(3.22 \times 10^4\)[/tex] into expanded form:
1. Multiply 3.22 by [tex]\(10^4\)[/tex] (10,000).
2. The result is 32200.
#### 10.2.2 [tex]\(3.22 \times 10^{-4}\)[/tex]
To convert [tex]\(3.22 \times 10^{-4}\)[/tex] into expanded form:
1. Multiply 3.22 by [tex]\(10^{-4}\)[/tex] (0.0001).
2. The result is 0.000322.
### 10.3 Simplify
To simplify [tex]\(-2 \times 10^{10} - 4 \times 10^9\)[/tex]:
1. Rewrite both terms to have the same powers of 10. The first term is already [tex]\(-2 \times 10^{10}\)[/tex]. Express the second term as [tex]\(-0.4 \times 10^{10}\)[/tex].
2. Combine the coefficients: [tex]\(-2 - 0.4 = -2.4\)[/tex].
3. The simplified expression is [tex]\(-2.4 \times 10^{10}\)[/tex], which is [tex]\(-24000000000\)[/tex].
These are the solutions for the given question. If you have any more questions, feel free to ask!
### 10.1 Write the following in scientific notation
#### 10.1.15 5133000000000
To convert 5133000000000 into scientific notation:
1. Place the decimal after the first non-zero digit: 5.133.
2. Count the number of places you moved the decimal. In this case, it's 12 places to the right.
3. Write the result as: [tex]\(5.133 \times 10^{12}\)[/tex].
#### 10.1.2. 0.0000006523
To convert 0.0000006523 into scientific notation:
1. Place the decimal after the first non-zero digit: 6.523.
2. Count the number of places you moved the decimal. Here, it is 7 places to the left.
3. Write the result as: [tex]\(6.523 \times 10^{-7}\)[/tex].
### 10.2 Write the following in expanded form
#### 10.2.1 [tex]\(3.22 \times 10^4\)[/tex]
To convert [tex]\(3.22 \times 10^4\)[/tex] into expanded form:
1. Multiply 3.22 by [tex]\(10^4\)[/tex] (10,000).
2. The result is 32200.
#### 10.2.2 [tex]\(3.22 \times 10^{-4}\)[/tex]
To convert [tex]\(3.22 \times 10^{-4}\)[/tex] into expanded form:
1. Multiply 3.22 by [tex]\(10^{-4}\)[/tex] (0.0001).
2. The result is 0.000322.
### 10.3 Simplify
To simplify [tex]\(-2 \times 10^{10} - 4 \times 10^9\)[/tex]:
1. Rewrite both terms to have the same powers of 10. The first term is already [tex]\(-2 \times 10^{10}\)[/tex]. Express the second term as [tex]\(-0.4 \times 10^{10}\)[/tex].
2. Combine the coefficients: [tex]\(-2 - 0.4 = -2.4\)[/tex].
3. The simplified expression is [tex]\(-2.4 \times 10^{10}\)[/tex], which is [tex]\(-24000000000\)[/tex].
These are the solutions for the given question. If you have any more questions, feel free to ask!
