Ordering fractions and decimals - Fraction and Decimal Worksheets ... - Free Printable

To solve these problems, we need to put the numbers in order from smallest to largest. The easiest way to do this is to change all the fractions into decimals.

Here is how to convert a fraction to a decimal: divide the top number (numerator) by the bottom number (denominator).

Problem 1
The numbers are: $0.2$, $\frac{3}{10}$, $\frac{1}{10}$, $0.25$, $\frac{11}{100}$

Let's convert the fractions:
* $\frac{3}{10} = 3 \div 10 = 0.3$
* $\frac{1}{10} = 1 \div 10 = 0.1$
* $\frac{11}{100} = 11 \div 100 = 0.11$

Now we have these decimals: $0.2$, $0.3$, $0.1$, $0.25$, $0.11$.

Let's order them from smallest to largest:
1. $0.1$ (which is $\frac{1}{10}$)
2. $0.11$ (which is $\frac{11}{100}$)
3. $0.2$
4. $0.25$
5. $0.3$ (which is $\frac{3}{10}$)

Problem 2
The numbers are: $0.3$, $\frac{3}{5}$, $\frac{4}{5}$, $0.7$, $\frac{85}{100}$

Let's convert the fractions:
* $\frac{3}{5} = 3 \div 5 = 0.6$
* $\frac{4}{5} = 4 \div 5 = 0.8$
* $\frac{85}{100} = 85 \div 100 = 0.85$

Now we have these decimals: $0.3$, $0.6$, $0.8$, $0.7$, $0.85$.

Let's order them from smallest to largest:
1. $0.3$
2. $0.6$ (which is $\frac{3}{5}$)
3. $0.7$
4. $0.8$ (which is $\frac{4}{5}$)
5. $0.85$ (which is $\frac{85}{100}$)

Problem 3
The numbers are: $\frac{3}{4}$, $\frac{3}{8}$, $0.77$, $0.61$, $\frac{8}{12}$

Let's convert the fractions:
* $\frac{3}{4} = 3 \div 4 = 0.75$
* $\frac{3}{8} = 3 \div 8 = 0.375$
* $\frac{8}{12}$ can be simplified to $\frac{2}{3}$ first, or just divide $8 \div 12$.
* $8 \div 12 = 0.666...$ (we can write this as approx $0.67$)

Now we have these decimals: $0.75$, $0.375$, $0.77$, $0.61$, $0.666...$

Let's order them from smallest to largest:
1. $0.375$ (which is $\frac{3}{8}$)
2. $0.61$
3. $0.666...$ (which is $\frac{8}{12}$)
4. $0.75$ (which is $\frac{3}{4}$)
5. $0.77$

Problem 4
The numbers are: $\frac{7}{5}$, $\frac{11}{8}$, $1.12$, $1.02$, $\frac{13}{10}$

Let's convert the fractions:
* $\frac{7}{5} = 7 \div 5 = 1.4$
* $\frac{11}{8} = 11 \div 8 = 1.375$
* $\frac{13}{10} = 13 \div 10 = 1.3$

Now we have these decimals: $1.4$, $1.375$, $1.12$, $1.02$, $1.3$.

Let's order them from smallest to largest:
1. $1.02$
2. $1.12$
3. $1.3$ (which is $\frac{13}{10}$)
4. $1.375$ (which is $\frac{11}{8}$)
5. $1.4$ (which is $\frac{7}{5}$)

Final Answer:
1. $\frac{1}{10}, \frac{11}{100}, 0.2, 0.25, \frac{3}{10}$
2. $0.3, \frac{3}{5}, 0.7, \frac{4}{5}, \frac{85}{100}$
3. $\frac{3}{8}, 0.61, \frac{8}{12}, \frac{3}{4}, 0.77$
4. $1.02, 1.12, \frac{13}{10}, \frac{11}{8}, \frac{7}{5}$