Fraction decimal percentage
Introduction :
A fraction is a part of a whole. A fraction can be altered to a decimal by dividing the upper number, or numerator, by the lower number, or denominator. Fractions are to indicate ratios, and to represent division which is one of the basic arithmetic operations.
A decimal number is a number which is a part of a whole number and a fractional whole number. For example, the decimal number 769.236 has a whole part of 769 and a fractional whole part of 236. The ( . ) is called the decimal point. The numbers to the left of the decimal point is the whole part of the number, and the numbers to the right of the decimal point is the fractional whole part of the number.
769.236 = 700 + 60 + 9 + 0.2 + 0.03 + 0.006 and is read as seven hundred sixty-nine and two-hundred and thirty-six thousandths, or seven hundred sixty-nine point two-three-six.
The word 'per cent' (or 'per centum') means ' per hundred' (or ' out of hundred').
Percentage implies calculation per every hundred. So, it is a fraction expressed with 100 as its denominator.
It is usually denoted by the symbol '%' or sometimes by 'p.c'.
Thus 5% = 5 out of hundred = $\frac{5}{100}$
Inter-relationship between Percentage, Fraction and Decimal:
Rule1: To convert a given percentage into a fraction (or a decimal), drop the symbol '%' and divide by 100.
Ex: (a) Express 15% as a fraction;
(b) Find 12 $\frac{1}{2}$ % of a Rs. 200
Sol: (a) 15% = $\frac{15}{100}$ = $\frac{3}{20}$
(b) 12 $\frac{1}{2}$ % = $\frac{25}{2}$ % = $\frac{25}{100}$ = $\frac{1}{8}$
There fore 12 $\frac{1}{2}$ % of a Rs. 200 = $\frac{1}{8}$ of Rs. 200 = Rs. $\frac{1}{8}$ × 200 = Rs. 25
Rule2: To convert a given fraction (or a decimal) into a percentage multiply by 100 and attach the '%' symbol to it.
Ex: (a) Express $\frac{2}{5}$ as a percentage;
(b) what percentage is Rs 20 of Rs. 125?
Sol: (a) $\frac{2}{5}$ = ($\frac{2}{5}$ × 100)% = 40%.
(b) The required percentage = ($\frac{20}{125}$ × 100)% = 16%
Example problems on percentage, fractions and decimals:
Ex1: Express 8$\frac{2}{5}$ % in the fraction, decimal and ratio.
Sol: Step1: 8$\frac{2}{5}$ % = $\frac{42}{5}$ % = $\frac{42}{5 × 100}$ = $\frac{21}{250}$ (in fraction)
Step2: = $\frac{21 × 4}{250 × 4}$ = 0.084 (in decimal)
Step3: = 21 : 250 (in ratio)
Ex2: Express $\frac{2}{3}$ , 0.36 as pecentages.
Sol: Step1: $\frac{2}{3}$ = ($\frac{2}{3}$ × 100)% = $\frac{200}{3}$ % = 66 $\frac{2}{3}$ %.
Step2: 0.36 = $\frac{36}{100}$ = ($\frac{36}{100}$ × 100)% = 36%.
Ex3: In an examination a student got 672 marks out of 800. Find out what percentage of the total marks he/she got?
Sol: Step1:Marks obtained by the student = 672
Step2: Total marks = 800
Step3: Therefore the required percentage of marks = ($\frac{672}{800}$ × 100)% = 84%.
Ex4: If 60% of the student in a school are boys and girls number is 812, how many boys are there?
Sol: Step1: 60% of the students are boys
Step2: Therefore (100 - 60) or 40% of the students are girls
Step3: Therefore 40% of the total number of students = 812
Step4: Therefore 60% of the total number of students = ($\frac{812}{40}$ × 60) = 1218.
Thus there are 1218 boys in the school.
Ex5: If A's income be 25% more than B's, how much percent is B's income less than A's?
Sol: Step1: Let the income of B = Rs. 100
Step2: Therefore A's income = 25% more than Rs. 100
= Rs. 100 + Rs. 25 = Rs. 125
Step3: If A's income is Rs. 125, then B's income = Rs. 100
Step4: If A's income is Rs. 100, then B's income = Rs. ($\frac{100}{125}$ × 100) = Rs. 80
Therefore B's income is less than A's income by Rs.(100 - 80) or Rs. 20
Step5: That is B's income is less than A's income by 20%.
Ex6: In an election only two candidates contested. The one who got 62% of the votes was elected by a majority of 144 votes. Find the total number of votes polled.
Sol: Step1:% votes got by the winning candidate = 62%.
Step2:% votes got by defeated candidates = (100 -62) % = 38%
Step3: Therefore the difference between the % votes got by the two candidates = (62 - 38)% = 24%
Step4: Therefore 24% of the total number of votes polled = 144
Step5: So 100% of the total number votes polled = $\frac{144}{24}$ × 100 = 600
Step6: Therefore total number of votes polled = 600.
Practice problems on percentage, fractions and decimals:
Pro1: Express the following percents into fractions and decimals.
(a) 20%
(b) 50 %
(c) 3$\frac{1}{8}$ %
Ans: a) $\frac{1}{5}$ in fraction, 0.2 in decimal
b) $\frac{1}{2}$ in fraction, 0.5 in decimal
c) $\frac{1}{32}$ in fraction, 0.03125 in decimal
Pro 2: In an examination a boys gets 348 marks out of 400. What is his percentage of marks in that examination?
Ans: 87%
I like to share this Fractions to Percentages with you all through my blog.
A fraction is a part of a whole. A fraction can be altered to a decimal by dividing the upper number, or numerator, by the lower number, or denominator. Fractions are to indicate ratios, and to represent division which is one of the basic arithmetic operations.
A decimal number is a number which is a part of a whole number and a fractional whole number. For example, the decimal number 769.236 has a whole part of 769 and a fractional whole part of 236. The ( . ) is called the decimal point. The numbers to the left of the decimal point is the whole part of the number, and the numbers to the right of the decimal point is the fractional whole part of the number.
769.236 = 700 + 60 + 9 + 0.2 + 0.03 + 0.006 and is read as seven hundred sixty-nine and two-hundred and thirty-six thousandths, or seven hundred sixty-nine point two-three-six.
The word 'per cent' (or 'per centum') means ' per hundred' (or ' out of hundred').
Percentage implies calculation per every hundred. So, it is a fraction expressed with 100 as its denominator.
It is usually denoted by the symbol '%' or sometimes by 'p.c'.
Thus 5% = 5 out of hundred = $\frac{5}{100}$
Inter-relationship between Percentage, Fraction and Decimal:
Rule1: To convert a given percentage into a fraction (or a decimal), drop the symbol '%' and divide by 100.
Ex: (a) Express 15% as a fraction;
(b) Find 12 $\frac{1}{2}$ % of a Rs. 200
Sol: (a) 15% = $\frac{15}{100}$ = $\frac{3}{20}$
(b) 12 $\frac{1}{2}$ % = $\frac{25}{2}$ % = $\frac{25}{100}$ = $\frac{1}{8}$
There fore 12 $\frac{1}{2}$ % of a Rs. 200 = $\frac{1}{8}$ of Rs. 200 = Rs. $\frac{1}{8}$ × 200 = Rs. 25
Rule2: To convert a given fraction (or a decimal) into a percentage multiply by 100 and attach the '%' symbol to it.
Ex: (a) Express $\frac{2}{5}$ as a percentage;
(b) what percentage is Rs 20 of Rs. 125?
Sol: (a) $\frac{2}{5}$ = ($\frac{2}{5}$ × 100)% = 40%.
(b) The required percentage = ($\frac{20}{125}$ × 100)% = 16%
Example problems on percentage, fractions and decimals:
Ex1: Express 8$\frac{2}{5}$ % in the fraction, decimal and ratio.
Sol: Step1: 8$\frac{2}{5}$ % = $\frac{42}{5}$ % = $\frac{42}{5 × 100}$ = $\frac{21}{250}$ (in fraction)
Step2: = $\frac{21 × 4}{250 × 4}$ = 0.084 (in decimal)
Step3: = 21 : 250 (in ratio)
Ex2: Express $\frac{2}{3}$ , 0.36 as pecentages.
Sol: Step1: $\frac{2}{3}$ = ($\frac{2}{3}$ × 100)% = $\frac{200}{3}$ % = 66 $\frac{2}{3}$ %.
Step2: 0.36 = $\frac{36}{100}$ = ($\frac{36}{100}$ × 100)% = 36%.
Ex3: In an examination a student got 672 marks out of 800. Find out what percentage of the total marks he/she got?
Sol: Step1:Marks obtained by the student = 672
Step2: Total marks = 800
Step3: Therefore the required percentage of marks = ($\frac{672}{800}$ × 100)% = 84%.
Ex4: If 60% of the student in a school are boys and girls number is 812, how many boys are there?
Sol: Step1: 60% of the students are boys
Step2: Therefore (100 - 60) or 40% of the students are girls
Step3: Therefore 40% of the total number of students = 812
Step4: Therefore 60% of the total number of students = ($\frac{812}{40}$ × 60) = 1218.
Thus there are 1218 boys in the school.
Ex5: If A's income be 25% more than B's, how much percent is B's income less than A's?
Sol: Step1: Let the income of B = Rs. 100
Step2: Therefore A's income = 25% more than Rs. 100
= Rs. 100 + Rs. 25 = Rs. 125
Step3: If A's income is Rs. 125, then B's income = Rs. 100
Step4: If A's income is Rs. 100, then B's income = Rs. ($\frac{100}{125}$ × 100) = Rs. 80
Therefore B's income is less than A's income by Rs.(100 - 80) or Rs. 20
Step5: That is B's income is less than A's income by 20%.
Ex6: In an election only two candidates contested. The one who got 62% of the votes was elected by a majority of 144 votes. Find the total number of votes polled.
Sol: Step1:% votes got by the winning candidate = 62%.
Step2:% votes got by defeated candidates = (100 -62) % = 38%
Step3: Therefore the difference between the % votes got by the two candidates = (62 - 38)% = 24%
Step4: Therefore 24% of the total number of votes polled = 144
Step5: So 100% of the total number votes polled = $\frac{144}{24}$ × 100 = 600
Step6: Therefore total number of votes polled = 600.
Practice problems on percentage, fractions and decimals:
Pro1: Express the following percents into fractions and decimals.
(a) 20%
(b) 50 %
(c) 3$\frac{1}{8}$ %
Ans: a) $\frac{1}{5}$ in fraction, 0.2 in decimal
b) $\frac{1}{2}$ in fraction, 0.5 in decimal
c) $\frac{1}{32}$ in fraction, 0.03125 in decimal
Pro 2: In an examination a boys gets 348 marks out of 400. What is his percentage of marks in that examination?
Ans: 87%
I like to share this Fractions to Percentages with you all through my blog.