Welcome to our Math lesson on The Meaning of Decimals. Converting Fractions into Decimals without a Calculator, this is the second lesson of our suite of math lessons covering the topic of Converting Fractions to Decimals and Vice-versa, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Decimals are an alternative representation of decimal mixed numbers. They are made of two parts: the left part which shows the whole part of the corresponding decimal mixed number and the right part which shows the numerator of the fractional part of the corresponding decimal mixed number. A dot known as decimal point separates the whole and decimal part of such numbers.
In other words, the decimal mixed number 3 7/10 is alternatively written as 3.7 where 3 shows the whole part of the corresponding mixed number and 7 the numerator of the fractional part of this number. In symbols, we write
and so on.
The number of zeroes in the denominator of the decimal mixed number determines the number of digits after the decimal point (we say "the number of decimal places"). Thus, if the denominator of the mixed number is 10, the corresponding decimal has one decimal place, if the denominator of the mixed number is 100, the corresponding decimal has two decimal places and so on.
Express the following mixed numbers as decimals.
As for the other fractions that cannot turn into decimal fractions, we apply the normal division of their numerator and denominator using the division method explained in tutorial 1.3. In most cases, this division gives an infinite number of digits after the decimal place but if you look them carefully, you will detect a kind of recurrence, i.e. the pattern is repeated after a number of digits. For example, when written as decimal, the fraction 3/7 becomes
As you see, the recurring part highlighted in yellow is repeated an infinity number of times as this decimal has no end. When we are completing the division by using the method described in tutorial 1.3 and we notice the repetition of two digits, it is quite probable that the recurrence has already began to appear. Let's consider an example in this regard.
Express the following fractions as decimals.
|Tutorial ID||Math Tutorial Title||Tutorial||Video|
|3.5||Converting Fractions to Decimals and Vice-versa|
|Lesson ID||Math Lesson Title||Lesson||Video|
|3.5.2||The Meaning of Decimals. Converting Fractions into Decimals without a Calculator|
|3.5.3||Converting Decimals to Fractions|
|3.5.4||Converting Recurrent Fractions into Decimals|
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