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Question Video: Answering a Word Problem Using Conversion between Fractions, Terminating Decimals, or Percentages Mathematics

A woman bought 4/20 kg of apples. She places these apples on a digital scale that displays their weight (in kilograms) as a decimal. What numbers should appear on the display of the digital scale?

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Video Transcript

A woman bought four twentieths of a kilogram of apples. She places these apples on a digital scale that displays their weight, in kilograms, as a decimal. What numbers should appear on the display of the digital scale?

In this question, we want to convert the given fraction to a decimal. The easiest way to do this is to simply divide the numerator four by the denominator 20 on a calculator. This gives us an answer of 0.2. However, it is also important to have a method we can use to convert from fractions to decimals by hand. We recall that the first three decimal places to the right of the decimal point are tenths, hundredths, and thousandths. This means that in order to convert a fraction to a terminating decimal, we can find an equivalent fraction where the denominator is equal to 10, 100, or 1000. When finding equivalent fractions, we must multiply or divide the denominator and numerator by the same amount. Since 20 divided by two is equal to 10, we must also divide the numerator by two. This means that the fraction four twentieths is equivalent to two-tenths. And as a decimal, we can write this as 0.2.

An alternative method would be to multiply the denominator by five to give an equivalent fraction with a denominator of 100. Since four multiplied by five is 20, four twentieths is equivalent to twenty hundredths. As a decimal, this is written as 0.20. And since twenty hundredths is equivalent to two-tenths, our final answer is 0.2. Four twentieths of a kilogram is equivalent to 0.2 kilograms.

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