Converting Decimals to Fractions
In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps:
Step I: Obtain the decimal.
Step II: Remove the decimal points from the given decimal and take as numerator.
Step III: At the same time write in the denominator, as many zero or zeros to the right of 1(one) (For example 10, 100 or 1000 etc.) as there are number of digit or digits in the decimal part. And then simplify it.
We can express a decimal number as a fraction by keeping the given number as the numerator without a decimal point and writing 1 in the denominator followed by as many zeroes on the right as the number of decimal places in the given decimal number has.
For example:
(i) 124.6 = \(\frac{1246}{10}\)
(ii) 12.46 = \(\frac{1246}{100}\)
(iii) 1.246 = \(\frac{1246}{1000}\)
The problem will help us to understand how to convert decimal into fraction.
In 0.7 we will change the decimal to
fraction.
First we will write the decimal
without the decimal point as the numerator.
Now in the denominator, write 1
followed by one zeros as there are 1 digit in the decimal part of the decimal
number.
= 7/10
Therefore, we observe that 0.7
(decimal) is converted to 7/10 (fraction).
Worked-out examples on converting decimals
to fractions:
1. Convert each of the following into fractions.
(i) 3.91
Solution:
3.91
Write the given decimal number
without the decimal point as numerator.
In the denominator, write 1
followed by two zeros as there are 2 digits in the decimal part of the decimal
number.
= 391/100
(ii) 2.017
Solution:
2.017
= 2.017/1
= 2.017 × 1000/1 × 1000 →
In the denominator, write 1 followed by three zeros as there are 3 digits in
the decimal part of the decimal number.
= 2017/1000
2. Convert 0.0035 into fraction in the simplest form.
Solution:
0.0035
Write the given decimal number
without the decimal point as numerator.
In the denominator, write 1
followed by four zeros to the right of 1 (one) as there are 4 decimal places in
the given decimal number.
Now we will reduce the fraction
35/10000 and obtained to its lowest term or the simplest form.
= 7/2000
3. Express the following decimals as fractions in lowest form:
(i) 0.05
Solution:
0.05
= 5/100 → Write
the given decimal number without the decimal point as numerator.
In the denominator, write 1
followed by two zeros to the right of 1 (one) as there are 2 decimal places in
the given decimal number.
= 5/100 ÷ 5/5 →
Reduce the fraction obtained to its lowest term.
= 1/20
(ii) 3.75
Solution:
3.75
= 375/100 → Write
the given decimal number without the decimal point as numerator.
In the denominator, write 1
followed by two zeros to the right of 1 (one) as there are 2 decimal places in
the given decimal number.
= 375/100 ÷ 25/25 → Reduce the fraction obtained to its simplest
form.
= 15/4
(iii) 0.004
Solution:
0.004
= 4/1000 → Write the given decimal number without the
decimal point as numerator.
In the denominator, write 1
followed by three zeros to the right of 1 (one) as there are 3 decimal places
in the given decimal number.
= 4/1000 ÷ 4/4 →
Reduce the fraction obtained to its lowest term.
= 1/250
(iv) 5.066
Solution:
5.066
= 5066/1000 → Write the given decimal number without the decimal point as numerator.
In the denominator, write 1 followed by three zeros to the right of 1 (one) as there are 3 decimal places in the given decimal number.
= 5066/1000 ÷ 2/2 → Reduce the fraction obtained to its simplest form.
= 2533/500
Practice Problems on Converting Decimals to Fractions:
1. Convert the given decimal numbers to fractions in the lowest
term:
(i) 1.3
(ii) 0.004
(iii) 4.005
(iv) 7.289
(v) 0.56
(vi) 21.08
(vii) 0.067
(viii) 6.66
Answers:
(i) \(\frac{13}{10}\)
(ii) \(\frac{1}{250}\)
(iii) \(\frac{801}{200}\)
(iv) \(\frac{7289}{1000}\)
(v) \(\frac{14}{25}\)
(vi) \(\frac{527}{25}\)
(vii) \(\frac{67}{1000}\)
(viii) \(\frac{333}{50}\)
You might like these
-
In 5th Grade Decimals Worksheet contains various types of questions on operations on decimal numbers. The questions are based on formation of decimals, comparing decimals, Converting Fractions to Decimals, Addition of decimals, subtraction of decimals, multiplication of
-
While comparing natural numbers we first compare total number of digits in both the numbers and if they are equal then we compare the digit at the extreme left. If they also equal then we compare the next digit and so on. We follow the same pattern while comparing the
-
Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is missing either in the integral part or decimal part, substitute with 0.
-
Division of a decimal number by 10, 100 or 1000 can be performed by moving the decimal point to the left by as many places as the number of zeroes in the divisor. The rules of division of decimal fractions by 10, 100, 1000 etc. are discussed here.
-
Addition of decimal numbers are similar to addition of whole numbers. We convert them to like decimals and place the numbers vertically one below the other in such a way that the decimal point lies exactly on the vertical line. Add as usual as we learnt in the case of whole
-
Simplification in decimals can be done with the help of PEMDAS Rule. From the above chart we can observe that first we have to work on "P or Parentheses" and then on "E or Exponents", then from
-
Solve the questions given in the worksheet on decimal word problems at your own space. This worksheet provides a mixture of questions on decimals involving order of operations
-
Practice the math questions given in the worksheet on dividing decimals. Divide the decimals to find the quotient, same like dividing whole numbers. This worksheet would be really good for the students to practice huge number of decimal division problems.
-
To divide a decimal number by a whole number the division is performed in the same way as in the whole numbers. We first divide the two numbers ignoring the decimal point and then place the decimal point in the quotient in the same position as in the dividend.
-
We will practice the questions given in the worksheet on multiplication of decimal fractions. While multiplying the decimal numbers ignore the decimal point and perform the multiplication as usual and then put the decimal point in the product to get as many decimal places in
-
To multiply a decimal number by a decimal number, we first multiply the two numbers ignoring the decimal points and then place the decimal point in the product in such a way that decimal places in the product is equal to the sum of the decimal places in the given numbers.
-
The rules of multiplying decimals are: (i) Take the two numbers as whole numbers (remove the decimal) and multiply. (ii) In the product, place the decimal point after leaving digits equal to the total number of decimal places in both numbers.
-
The working rule of multiplication of a decimal by 10, 100, 1000, etc... are: When the multiplier is 10, 100 or 1000, we move the decimal point to the right by as many places as number of zeroes after 1 in the multiplier.
-
We will practice the questions given in the worksheet on subtraction of decimal fractions. While subtracting the decimal numbers convert them into like decimal then subtract as usual ignoring decimal point and then put the decimal point in the difference directly under the
-
We will practice the questions given in the worksheet on addition of decimal fractions. While adding the decimal numbers convert them into like decimal then add as usual ignoring decimal point and then put the decimal point in the sum directly under the decimal points of all
-
The rules of subtracting decimal numbers are: (i) Write the digits of the given numbers one below the other such that the decimal points are in the same vertical line. (ii) Subtract as we subtract whole numbers. Let us consider some of the examples on subtraction
-
Practice different types of math questions given in the worksheet on comparing and ordering decimals. This worksheet contains questions mainly related to compare decimals and then place the decimals in the correct order by arranging decimals in ascending order and desce
-
Like Decimal Fractions are discussed here. Two or more decimal fractions are called like decimals if they have equal number of decimal places. However the number of digits in the integral part does not matter. 0.43, 10.41, 183.42, 1.81, 0.31 are all like fractions
-
We will discuss here about changing unlike to like decimal fractions. Unlike decimal fractions can be changed to like decimals by adding as many zeroes as required. Convert 13.183, 341.43, 1.04 to like decimals.
-
Unlike decimal fractions are discussed here. Two or more decimal fractions are called unlike decimals if they have unequal numbers of decimal places. Let us consider some of the unlike decimals; (i) 8.4, 8.41, 8.412 In 8.4, 8.41, 8.412 the number of decimal places are 1, 2
● Related Concept
● Decimals
● Decimal Numbers
● Decimal Fractions
● Like and Unlike
Decimals
● Comparing Decimals
● Decimal Places
● Conversion of
Unlike Decimals to Like Decimals
● Decimal and
Fractional Expansion
● Terminating Decimal
● Non-Terminating
Decimal
● Converting Decimals
to Fractions
● Converting
Fractions to Decimals
● H.C.F. and L.C.M.
of Decimals
● Repeating or
Recurring Decimal
● Pure Recurring
Decimal
● Mixed Recurring
Decimal
● BODMAS Rule
● BODMAS/PEMDAS Rules
- Involving Decimals
● PEMDAS Rules -
Involving Integers
● PEMDAS Rules -
Involving Decimals
● PEMDAS Rule
● BODMAS Rules -
Involving Integers
● Conversion of Pure
Recurring Decimal into Vulgar Fraction
● Conversion of Mixed
Recurring Decimals into Vulgar Fractions
● Simplification of
Decimal
● Rounding Decimals
● Rounding Decimals
to the Nearest Whole Number
● Rounding Decimals
to the Nearest Tenths
● Rounding Decimals
to the Nearest Hundredths
● Round a Decimal
● Adding Decimals
● Subtracting
Decimals
● Simplify Decimals
Involving Addition and Subtraction Decimals
● Multiplying Decimal
by a Decimal Number
● Multiplying Decimal
by a Whole Number
● Dividing Decimal by
a Whole Number
● Dividing Decimal by
a Decimal Number
7th Grade Math Problems
From Converting Decimals to Fractions to HOME PAGE
Didn't find what you were looking for? Or want to know more information
about Math Only Math.
Use this Google Search to find what you need.
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.