- Solution for Converting.2 in the Fraction is 0.2 = 2 / 10 Below is the Representation of.2 as a Fraction in Graph format. Please Enter Zero Before The Decimal Number Like(0.1,0.34,0.xyz values) Just Type In A Decimal Number.
- 0.2 is a repeating decimal number and you want to convert it to a fraction or mixed number. When you say 0.2 repeating, you mean that the 1 is repeating. Here is the question formulated in mathematical terms with the vinculum line above the decimal number that is repeating. 2 repeating as a fraction.
- 1 6% As A Fraction
- 0.6% As A Fraction
- Write 0.4 As A Fraction
- Write 6 2/3 As A Fraction In Simplest Form
To write 2.6 as a fraction you have to write 2.6 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number. 2.6 = 2.6/1 = 26/10 And finally we have: 2.6 as a fraction equals 26/10. You can always share this solution.
Alignments to Content Standards:5.NF.A.1
Task
Ancient Egyptians used unit fractions, such as $frac{1}{2}$ and $frac{1}{3}$,to represent all fractions. For example, they might write the number $frac{2}{3}$ as $frac{1}{2} + frac{1}{6}$.
Motorsport manager 1 5. We often think of $frac{2}{3}$ as $frac{1}{3}+frac{1}{3}$, but the ancient Egyptians would not write it this way because they didn't use the same unit fraction twice.
- Write each of the following Egyptian fractions as a single fraction:
- $frac{1}{2} + frac{1}{3}$,
- $frac{1}{2}+ frac{1}{3} + frac{1}{5}$,
- $frac{1}{4} + frac{1}{5} + frac{1}{12}$.
- How might the ancient Egyptians have writen the fraction we write as $frac{3}{4}$?
IM Commentary
One goal of this task is to help students develop comfort and ease with adding fractions with unlike denominators. Another goal is to help them develop fraction number sense by having students decompose fractions. Because the Egyptians represented fractions differently than we do, it can also help students understand that there can be many ways of representing the same number. This helps prepare them for writing algebraic expressions in 6th grade.This task is an instructional task; the teacher may wish to supplement part (b) of the question in two directions:
- As is indicated in the solution, there are many ways to write $frac{3}{4}$ as a sum of unit fractions and student work may naturally lead to a discussion of this issue.
- Students might be prompted to try to express some other fractions, suchas $frac{2}{5}$ or $frac{3}{5}$ as sums of unit fractions.
For historical accuracy, it should be noted that the ancient Egyptians hadspecial hieroglyphic symbols for the two fractions $frac{2}{3}$ and $frac{3}{4}$considered in this problem. In general, however, they used tables in orderto break down fractions into sums of unit fractions.
One issue which comes up in the solution is that there are apparently manyways to write an Egyptian fraction. This leads to an interesting question: how do you find the 'best' Egyptian fraction representing a given fraction? Here a reasonable interpretation of 'best' would be one which has the smallest number of unit fractions. This problem will be addressed in a second task which falls under the high school algebra standards.
Solution
- For the Egyptian fraction $frac{1}{2} + frac{1}{3}$, a common denominatorwould be $6$ since $6$ is divisible by both $2$ and $3$. Converting tothis common denominator we findbegin{align}frac{1}{2} + frac{1}{3} &= frac{3 times 1}{3 times 2} + frac{2 times 1}{2 times 3} &= frac{3}{6} + frac{2}{6} &= frac{5}{6}.end{align}For $frac{1}{2} + frac{1}{3} + frac{1}{5}$ we could use what we have just found,namely that $frac{1}{2} + frac{1}{3} = frac{5}{6}$. To add $frac{5}{6}$ and$frac{1}{5}$ we can use $5 times 6 = 30$as a common denominator:begin{align}frac{1}{2} + frac{1}{3} + frac{1}{5} &= frac{5}{6} + frac{1}{5} &= frac{5 times 5}{5 times 6} + frac{6 times 1}{6 times 5} &= frac{25 + 6}{30} &= frac{31}{30}.end{align}For $frac{1}{4}$, $frac{1}{5}$, and $frac{1}{12}$ note that $12$ is divisibleby $4$ so we can look for a common denominator of $frac{1}{5}$ and $frac{1}{12}$ and thiswill also work with $frac{1}{4}$. For $frac{1}{5}$ and $frac{1}{12}$ we canuse $5 times 12$ as a common denominator:begin{align}frac{1}{4} + frac{1}{5} + frac{1}{12} &= frac{15 times 1}{15 times 4} + frac{12 times 1}{12 times 5} + frac{5 times 1}{5 times 12} &= frac{15}{60} + frac{12}{60} + frac{5}{60} &= frac{15+12+5}{60} &= frac{32}{60}.end{align}As a parenthetical note, this gives an example where even though we found theleast common denominator to perform the addition, the resulting fractionis not in reduced form: the reduced form is $frac{8}{15}$.
- To write $frac{3}{4}$ as an Egyptian fraction, we might notice thatbegin{align}frac{3}{4} &= frac{2+1}{4} &= frac{2}{4} + frac{1}{4} &= frac{1}{2} + frac{1}{4}.end{align}Alternatively, since $frac{1}{2}$ is the largest of the unit fractions that isless than $frac{3}{4}$ it would be reasonable to take $frac{1}{2}$ as oneof the unit fractions in the Egyptian fraction expression for $frac{3}{4}$. Performing subtraction givesbegin{align}frac{3}{4} - frac{1}{2} &= frac{3}{4} - frac{2 times 1}{2 times 2} &= frac{3}{4} - frac{2}{4} &= frac{1}{4}.end{align}This gives us the same expression as above: $frac{3}{4} = frac{1}{2} + frac{1}{4}$.There are many other ways to write $frac{3}{4}$ as an Egyptian fraction.Sincebegin{align}frac{1}{2} &= frac{3}{6} &= frac{2}{6} + frac{1}{6} &= frac{1}{3} + frac{1}{6}end{align}and since $frac{3}{4} = frac{1}{2} + frac{1}{4}$ we have another expression of$frac{3}{4}$ as an Egyptian fraction, namely$$frac{3}{4} = frac{1}{3} + frac{1}{6} + frac{1}{4}.$$All Egyptian fractions share this same property: there are always endless waysto write an Egyptian fraction.
Egyptian Fractions
Ancient Egyptians used unit fractions, such as $frac{1}{2}$ and $frac{1}{3}$,to represent all fractions. For example, they might write the number $frac{2}{3}$ as $frac{1}{2} + frac{1}{6}$.
We often think of $frac{2}{3}$ as $frac{1}{3}+frac{1}{3}$, but the ancient Egyptians would not write it this way because they didn't use the same unit fraction twice.
- Write each of the following Egyptian fractions as a single fraction:
- $frac{1}{2} + frac{1}{3}$,
- $frac{1}{2}+ frac{1}{3} + frac{1}{5}$,
- $frac{1}{4} + frac{1}{5} + frac{1}{12}$.
- How might the ancient Egyptians have writen the fraction we write as $frac{3}{4}$?
0.6 is a repeating decimal number and you want to convert it to a fraction or mixed number. When you say 0.6 repeating, you mean that the 1 is repeating. Here is the question formulated in mathematical terms with the vinculum line above the decimal number that is repeating.
0.6 repeating as a fraction
The formula to convert any repeating decimal number to a fraction is as follows:
DN = Decimal Number
F = 10 if one repeating number, 100 if two repeating numbers, 1000 if three repeating numbers, etc.
NRP = Non-repeating part of decimal number.
D = 9 if one repeating number, 99 if two repeating numbers, 999 if three repeating numbers, etc.
Below shows you how to get the answer to 0.6 repeating as a fraction using our formula.
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Below is the answer in the simplest form possible:
0.6 repeating as a fraction
1 6% As A Fraction
= 2/3
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