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6. Convert to scientific notation:
a. 4,230
b. 1.5 billion
c. 0.000247
d. 0.67 trillion
e. 121 million

7. Express in standard notation:
a. [tex]$4.8 \times 10^4$[/tex]
b. [tex]$5.7 \times 10^{-2}$[/tex]
c. A country predicts highway infrastructure improvements will cost [tex]$\$[/tex] 6 \times 10^{11}$. Write the value in decimal notation.

Sagot :

GinnyAnsweridn
Let's address each part of the question one by one.

### Part 6: Convert to Scientific Notation

#### a. 4,230
To convert 4,230 to scientific notation:
- Identify the significant figures: 4.23
- Count the number of places the decimal point needs to move to the left to get back to the original number: 3
- Therefore, 4,230 in scientific notation is [tex]\( 4.23 \times 10^3 \)[/tex].

#### b. 1.5 billion
To convert 1.5 billion to scientific notation:
- Recall that "billion" is [tex]\( 10^9 \)[/tex].
- Therefore, 1.5 billion is [tex]\( 1.5 \times 10^9 \)[/tex].

#### c. 0.000247
To convert 0.000247 to scientific notation:
- Identify the significant figures: 2.47
- Count the number of places the decimal point needs to move to the right to get back to the original number: 4
- Therefore, 0.000247 in scientific notation is [tex]\( 2.47 \times 10^{-4} \)[/tex].

#### d. 0.67 trillion
To convert 0.67 trillion to scientific notation:
- Recall that "trillion" is [tex]\( 10^{12} \)[/tex].
- Therefore, 0.67 trillion is [tex]\( 6.7 \times 10^{11} \)[/tex].

#### e. 121 million
To convert 121 million to scientific notation:
- Recall that "million" is [tex]\( 10^{6} \)[/tex].
- Identify the significant figures: 1.21
- Therefore, 121 million is [tex]\( 1.21 \times 10^8 \)[/tex] (since 121 million equals 121 multiplied by [tex]\(10^6\)[/tex]).

Summarizing the results for part 6:
- a: [tex]\( 4.23 \times 10^3 \)[/tex]
- b: [tex]\( 1.5 \times 10^9 \)[/tex]
- c: [tex]\( 2.47 \times 10^{-4} \)[/tex]
- d: [tex]\( 6.7 \times 10^{11} \)[/tex]
- e: [tex]\( 1.21 \times 10^8 \)[/tex]

### Part 7: Express in Standard Notation

#### a. [tex]\( 4.8 \times 10^4 \)[/tex]
To convert [tex]\( 4.8 \times 10^4 \)[/tex] to standard notation:
- Move the decimal point 4 places to the right.
- Therefore, [tex]\( 4.8 \times 10^4 \)[/tex] in standard notation is 48,000.

#### b. [tex]\( 5.7 \times 10^{-2} \)[/tex]
To convert [tex]\( 5.7 \times 10^{-2} \)[/tex] to standard notation:
- Move the decimal point 2 places to the left.
- Therefore, [tex]\( 5.7 \times 10^{-2} \)[/tex] in standard notation is 0.057.

#### c. [tex]\( 6 \times 10^{11} \)[/tex]
To convert [tex]\( 6 \times 10^{11} \)[/tex] to standard notation:
- Move the decimal point 11 places to the right.
- Therefore, [tex]\( 6 \times 10^{11} \)[/tex] in standard notation is 600,000,000,000.

Summarizing the results for part 7:
- a: 48,000
- b: 0.057
- c: 600,000,000,000
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