Final answer:
A rational number is converted to a decimal by dividing the numerator by the denominator. A decimal can become a percent by multiplying by 100, and a percent to a decimal by dividing by 100. Scientific notation is used for very small or large numbers, and when rounding after calculations, match the number of decimal places to the least certain value.
Step-by-step explanation:
To write a rational number as a decimal, you need to understand that a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not being zero. For instance, if we want to convert the rational number 3/4 into a decimal, we divide the numerator by the denominator. Using a calculator or long division, we find that 3 ÷ 4 = 0.75, which is the decimal representation of the fraction 3/4.
To express a decimal as a percent, we can write the decimal number as a fraction with 100 as the denominator. For example, the decimal 0.75 becomes 75/100. This fraction is then easily seen as 75%, because percents are simply fractions with a denominator of 100.
Converting a percent to a decimal involves writing the percent value as a fraction over 100 and then performing the division. For instance, 48% as a decimal is simply 48 ÷ 100, which equals 0.48.
When working with extremely small or large numbers, they can be written in scientific notation. For example, 0.0000045 can be written as 4.5 x 10-6. The coefficient here is 4.5, and the power of 10 indicates how many places the decimal point must move to retrieve the original number.
To convert a number like 0.0479 to a number from 1 to 10, we would move the decimal point until it is to the right of the first non-zero digit, resulting in 4.79 × 10-2 in scientific notation.
For calculating combined operations or when entering data into a linear equation, rounding may be required. Always round the result to the same number of decimal places as the least certain value (the number with the least number of decimal places). For example, if adding 1.2345 and 2.3, we would round the result to one decimal place, the least certain value.