Answer :
Sure! Let's write the given numbers in scientific notation step by step.
### (a) 0.0067
To express a number in scientific notation, we need to write it in the form:
[tex]\[ a \times 10^n \][/tex]
where [tex]\( a \)[/tex] is a number between 1 and 10, and [tex]\( n \)[/tex] is an integer.
1. Identify the significant digits: 6.7
2. Determine how many places the decimal point moves to the right to reach 6.7. That's 3 places.
3. Since the original number is less than 1, our exponent will be negative.
So, 0.0067 in scientific notation is:
[tex]\[ 6.7 \times 10^{-3} \][/tex]
### (b) 6500
Here we do a similar process:
1. Identify the significant digits: 6.5
2. Move the decimal point 3 places to the left so that the number becomes a value between 1 and 10.
3. Since the number is greater than 1, the exponent will be positive.
Thus, 6500 in scientific notation is:
[tex]\[ 6.5 \times 10^{3} \][/tex]
### (c) 7000
Again, follow the steps:
1. Identify the significant digits: 7
2. Move the decimal point 3 places to the left, which results in a number between 1 and 10.
3. The original number is greater than 1, so the exponent is positive.
Therefore, 7000 in scientific notation is:
[tex]\[ 7 \times 10^{3} \][/tex]
That's how you convert each number to scientific notation!
### (a) 0.0067
To express a number in scientific notation, we need to write it in the form:
[tex]\[ a \times 10^n \][/tex]
where [tex]\( a \)[/tex] is a number between 1 and 10, and [tex]\( n \)[/tex] is an integer.
1. Identify the significant digits: 6.7
2. Determine how many places the decimal point moves to the right to reach 6.7. That's 3 places.
3. Since the original number is less than 1, our exponent will be negative.
So, 0.0067 in scientific notation is:
[tex]\[ 6.7 \times 10^{-3} \][/tex]
### (b) 6500
Here we do a similar process:
1. Identify the significant digits: 6.5
2. Move the decimal point 3 places to the left so that the number becomes a value between 1 and 10.
3. Since the number is greater than 1, the exponent will be positive.
Thus, 6500 in scientific notation is:
[tex]\[ 6.5 \times 10^{3} \][/tex]
### (c) 7000
Again, follow the steps:
1. Identify the significant digits: 7
2. Move the decimal point 3 places to the left, which results in a number between 1 and 10.
3. The original number is greater than 1, so the exponent is positive.
Therefore, 7000 in scientific notation is:
[tex]\[ 7 \times 10^{3} \][/tex]
That's how you convert each number to scientific notation!
