Convert Decimal to Fraction
Numbers which we use in a normal calculation like 0,1,3, \(\frac{5}{4}\), etc are the real numbers. They can be both positive or negative. Real numbers are of two types – rational and irrational numbers. You will learn to convert decimal to fraction in this article easily.
We can express rational numbers in fractional format, but we cannot write an irrational number in fractional form. Numbers like \(\sqrt{3}\), \(\sqrt{2}\), \(\sqrt{5}\), etc whose square we cannot calculate are irrational.
Other numbers like \(\sqrt{4}\), 2, 3, – 3, \(\frac{7}{12}\), etc are rational numbers. We can represent rational numbers in fractional form. In a fraction, \(\frac{p}{q}\) where, (q≠0), p is the numerator and q is the denominator.
In the fraction if p is smaller than q (p<q), then we call it proper fraction like \(\frac{7}{11}\), \(\frac{13}{29}\), \(\frac{1}{6}\), etc. On the other hand, improper fractions are those in which denominator is greater than the numerator like \(\frac{19}{5}\), \(\frac{18}{11}\), etc which we can further write in the form of mixed fraction. Here, we will discuss the decimal fraction and will know how to convert decimal to fraction.
What is a Decimal Fraction?
It is a fraction in which the denominator of any rational number is in the power of 10 (like 10, 100, 1000 10⁴… etc).
For example – \(\frac{7}{100}\), \(\frac{3}{10}\), etc. Now what does that mean? Thus, \(\frac{7}{100}\) means 100th part of 7 units, \(\frac{3}{10}\) means 10th part of 3 units.
Easy Way to Convert Fraction to Decimal
If there is a decimal number 0.3, we read it as decimal 3. We should note here that 0.071 is not read as decimal zero seventy-one or simply zero seventy-one. Every digit after decimal must be read one by one. Decimal seventy one does not have any meaning.
Learn more about Decimal Fractions here in detail.
Converting Decimal to Common Fraction
Let’s take a look at how to convert decimal to fraction. Suppose we need to write 2.304 in decimal fraction. Since there are three digits after decimal so the denominator will be 10³=1000. So the fraction will be \(\frac{2304}{1000}\). We replace decimal with 1 in the denominator and write zero for each number after the decimal.
If we put zero after last significant digit of a decimal quantity it will not change the value of number or fraction. For example – 0.8 = \(\frac{8}{10}\), 0.80 = \(\frac{80}{100}\) = \(\frac{8}{10}\). We take 1, 2, 3, 4, 5, 6, 7, 8, 9 as significant digits while zero is not taken as a significant digit.
Multiplying a Decimal Fraction by Another Decimal Fraction
Let, we have to find the value of 17.234 × 11.8. To get the product, first, we will multiply 17234 × 118 and then put decimal after4 digits from the right side as there are three digits after decimal in the first number and 1 digit after the decimal in the second number. So there is a total of 4 numbers after the decimal.
Or, 17234 × 118 = 2033612, 17.234×11.8 = 203.3612
Solved Question for You
Q- How can we find the HCF and LCM of a decimal fraction?
Ans – Suppose we have to find the LCM and HCF of 0.36, 1.2 and 0.144. First, we will write all the numbers in such a way that the number of digits after the decimal is equal. Like, 0.360 for 0.36 and 1.200 for 1.2.
Now remove the decimals and find the LCM and HCF of these numbers. Here the numbers are 360, 1200, 144. The LCM will come as 3600 and HCF as 24. Since there are three digits after decimal in every number so we will put decimal after 3 digits from the right side. So the required HCF is 0.024 and LCM is 3.600 or 3.6.
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