Final answer:
When multiplying by a power of ten, we can simply move the decimal point to the right for each zero in the power of ten. Moving the decimal point left denotes a positive exponent, while moving it right indicates a negative exponent. This is essential for operations involving powers of ten and for expressing numbers in scientific notation.
Step-by-step explanation:
If a decimal point is only in the divisor (the number you are dividing by), you can move it up into the quotient (the result of the division). Let's consider an example where we need to multiply a decimal number by a power of ten.
For instance, if we are to multiply 2.4 by 100, we need to move the decimal point two places to the right. In the event that there are not enough decimal places, we use zeros as placeholders. Therefore, multiplying 2.4 by 100 results in:
2.4 x 100 = 240
When we move the decimal point to the left by n places, we say that n is positive. Conversely, when we move the decimal point to the right by n places, n is considered negative.
To express numbers in scientific notation, we often move the decimal point. For the number 12,700,000, we move the decimal to obtain 1.27, changing the large number into a more manageable form: 1.27 x 10^7. For very small numbers, like 0.000,006, we move the decimal six places to the left to obtain 6 x 10^-6. These coefficients (1.27 and 6) are used in scientific notation to simplify the expression of very large or very small numbers.
In summary, understanding how to move the decimal point is crucial in mathematics, particularly for operations involving powers of ten or when expressing numbers in scientific notation. Remember, we keep track of the number of places we moved the decimal point by expressing it as a power of ten.