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Sagot :
Sure, let's convert each of the given numbers into scientific notation in a step-by-step manner.
### a. 4,230
First, identify where the decimal point is. For 4,230, it's at the end of the number (4230).
Move the decimal point three places to the left to get a number between 1 and 10.
[tex]\[ 4,230 \rightarrow 4.230 \times 10^3 \][/tex]
In scientific notation, this is written as:
[tex]\[ 4.23 \times 10^3 \][/tex]
### b. 1.5 billion
"Billion" is represented as [tex]\( 10^9 \)[/tex]. Therefore, 1.5 billion can be written directly as:
[tex]\[ 1.5 \times 10^9 \][/tex]
In scientific notation, this is:
[tex]\[ 1.50 \times 10^9 \][/tex]
### c. 0.000247
For the number 0.000247, move the decimal point four places to the right to get a number between 1 and 10.
[tex]\[ 0.000247 \rightarrow 2.47 \times 10^{-4} \][/tex]
In scientific notation, this becomes:
[tex]\[ 2.47 \times 10^{-4} \][/tex]
### d. 0.67 trillion
"Trillion" is represented as [tex]\( 10^{12} \)[/tex]. Therefore, 0.67 trillion can be written as:
[tex]\[ 0.67 \times 10^{12} \][/tex]
Move the decimal point two places to the right to get a number between 1 and 10.
[tex]\[ 0.67 \rightarrow 6.7 \times 10^{11} \][/tex]
In scientific notation, this is:
[tex]\[ 6.70 \times 10^{11} \][/tex]
### e. 121 million
"Million" is represented as [tex]\( 10^6 \)[/tex]. Therefore, 121 million can be written as:
[tex]\[ 121 \times 10^6 \][/tex]
Move the decimal point two places to the left to get a number between 1 and 10.
[tex]\[ 121 \rightarrow 1.21 \times 10^8 \][/tex]
In scientific notation, this is:
[tex]\[ 1.21 \times 10^8 \][/tex]
### Final Scientific Notation Form
Summarizing the conversions:
a. [tex]\( 4,230 = 4.23 \times 10^3 \)[/tex]
b. [tex]\( 1.5 \text{ billion} = 1.50 \times 10^9 \)[/tex]
c. [tex]\( 0.000247 = 2.47 \times 10^{-4} \)[/tex]
d. [tex]\( 0.67 \text{ trillion} = 6.70 \times 10^{11} \)[/tex]
e. [tex]\( 121 \text{ million} = 1.21 \times 10^8 \)[/tex]
These are the steps to convert each number into scientific notation.
### a. 4,230
First, identify where the decimal point is. For 4,230, it's at the end of the number (4230).
Move the decimal point three places to the left to get a number between 1 and 10.
[tex]\[ 4,230 \rightarrow 4.230 \times 10^3 \][/tex]
In scientific notation, this is written as:
[tex]\[ 4.23 \times 10^3 \][/tex]
### b. 1.5 billion
"Billion" is represented as [tex]\( 10^9 \)[/tex]. Therefore, 1.5 billion can be written directly as:
[tex]\[ 1.5 \times 10^9 \][/tex]
In scientific notation, this is:
[tex]\[ 1.50 \times 10^9 \][/tex]
### c. 0.000247
For the number 0.000247, move the decimal point four places to the right to get a number between 1 and 10.
[tex]\[ 0.000247 \rightarrow 2.47 \times 10^{-4} \][/tex]
In scientific notation, this becomes:
[tex]\[ 2.47 \times 10^{-4} \][/tex]
### d. 0.67 trillion
"Trillion" is represented as [tex]\( 10^{12} \)[/tex]. Therefore, 0.67 trillion can be written as:
[tex]\[ 0.67 \times 10^{12} \][/tex]
Move the decimal point two places to the right to get a number between 1 and 10.
[tex]\[ 0.67 \rightarrow 6.7 \times 10^{11} \][/tex]
In scientific notation, this is:
[tex]\[ 6.70 \times 10^{11} \][/tex]
### e. 121 million
"Million" is represented as [tex]\( 10^6 \)[/tex]. Therefore, 121 million can be written as:
[tex]\[ 121 \times 10^6 \][/tex]
Move the decimal point two places to the left to get a number between 1 and 10.
[tex]\[ 121 \rightarrow 1.21 \times 10^8 \][/tex]
In scientific notation, this is:
[tex]\[ 1.21 \times 10^8 \][/tex]
### Final Scientific Notation Form
Summarizing the conversions:
a. [tex]\( 4,230 = 4.23 \times 10^3 \)[/tex]
b. [tex]\( 1.5 \text{ billion} = 1.50 \times 10^9 \)[/tex]
c. [tex]\( 0.000247 = 2.47 \times 10^{-4} \)[/tex]
d. [tex]\( 0.67 \text{ trillion} = 6.70 \times 10^{11} \)[/tex]
e. [tex]\( 121 \text{ million} = 1.21 \times 10^8 \)[/tex]
These are the steps to convert each number into scientific notation.
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