Final answer:
Numbers are converted into scientific notation by placing the decimal point after the first non-zero digit and adjusting the exponent of 10 accordingly. For example, 345.1 × 10² in proper scientific notation is 3.451 × 10´ and 0.000006567 becomes 6.567 × 10⁻⁶.
Step-by-step explanation:
In scientific notation, numbers are expressed with one non-zero digit before the decimal point, followed by a decimal fraction, and then exponentiated by 10 to a power. For instance:
- The number 345.1 × 10² is not in proper scientific notation because 345.1 is greater than 10. In proper scientific notation, this number should be 3.451 × 10´, because we have to move the decimal point two places to the left, which increases the exponent by two.
- As for 0.234 × 10-3, it also needs to have the decimal moved to be after the first significant digit, which would result in 2.34 × 10-4.
- Similarly, 1,800 × 10-2 needs to be rewritten as 1.8 × 10² because we have moved the decimal point three places to the left and subtracted three from the exponent to balance it.
The number 6.022 × 10²³ in standard notation is a very large number, having 23 zeros after the 6022.
When converting a number into scientific notation, such as 0.000006567, we find the first non-zero digit and place the decimal point immediately after it which gives us 6.567. We then count how many places the decimal point has been moved, which in this case is 6 places to the right making it 6.567 × 10⁻⁶.