Examples with solutions for Comparing Decimal Fractions: Comparison to simple fractions

Exercise #1

Choose the appropriate sign:

45?0.8 \frac{4}{5}?0.8

Video Solution

Step-by-Step Solution

First, let's convert 0.8 to a simple fraction.

Since there is only one number after the decimal point, the number is divided by 10 as follows:

0.8=810 0.8=\frac{8}{10}

Let's simplify the fraction so that we have two fractions with the same denominator:

8:210:2=45 \frac{8:2}{10:2}=\frac{4}{5}

Now we can compare and see that:

45=45 \frac{4}{5}=\frac{4}{5}

Answer

= =

Exercise #2

Choose the appropriate sign:

23?0.6 \frac{2}{3}?0.6

Video Solution

Step-by-Step Solution

First, let's convert 0.6 to a simple fraction.

Since there is only one digit after the decimal point, the number is divided by 10 as follows:

0.6=610 0.6=\frac{6}{10}

Let's reduce the fraction:

6:210:2=35 \frac{6:2}{10:2}=\frac{3}{5}

Now we have two simple fractions with different denominators.

To compare them, note that the smallest common denominator between them is 15.

We'll multiply each one to reach the common denominator as follows:

23×55=1015 \frac{2}{3}\times\frac{5}{5}=\frac{10}{15}

35×33=915 \frac{3}{5}\times\frac{3}{3}=\frac{9}{15}

Now we can compare the two fractions and see that:

\frac{10}{15}>\frac{9}{15}

Answer

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Exercise #3

Choose the appropriate sign:

34?0.8 \frac{3}{4}?0.8

Video Solution

Step-by-Step Solution

First, let's convert 0.8 to a simple fraction.

Since there is only one number after the decimal point, the number is divided by 10 as follows:

0.8=810 0.8=\frac{8}{10}

Let's reduce the fraction:

8:210:2=45 \frac{8:2}{10:2}=\frac{4}{5}

Now we have two simple fractions with different denominators.

To compare them, note that the smallest common denominator between them is 20.

We'll multiply each one to reach the common denominator as follows:

34×55=1520 \frac{3}{4}\times\frac{5}{5}=\frac{15}{20}

45×44=1620 \frac{4}{5}\times\frac{4}{4}=\frac{16}{20}

Now we can compare the two fractions and see that:

\frac{15}{20}<\frac{16}{20}

Answer

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Exercise #4

Choose the appropriate sign:

13?0.3 \frac{1}{3}?0.3

Video Solution

Step-by-Step Solution

First, let's convert 0.3 to a simple fraction.

Since there is only one number after the decimal point, the number divides by 10 as follows:

0.3=310 0.3=\frac{3}{10}

Now we have two simple fractions with different denominators.

To compare them, note that the smallest common denominator between them is 30.

We'll multiply each one to reach the common denominator as follows:

13×1010=1030 \frac{1}{3}\times\frac{10}{10}=\frac{10}{30}

310×33=930 \frac{3}{10}\times\frac{3}{3}=\frac{9}{30}

Now we can compare the two fractions and see that:

\frac{10}{30}>\frac{9}{30}

Answer

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Exercise #5

Choose the appropriate sign:

48?0.5 \frac{4}{8}?0.5

Video Solution

Step-by-Step Solution

First, let's convert 0.5 to a simple fraction.

Since there is only one digit after the decimal point, the number is divided by 10 as follows:

0.5=510 0.5=\frac{5}{10}

Now we have two simple fractions with different denominators.

To compare them, note that the smallest common denominator between them is 2.

We'll divide each one to reach the common denominator as follows:

48:44=12 \frac{4}{8}:\frac{4}{4}=\frac{1}{2}

510:55=12 \frac{5}{10}:\frac{5}{5}=\frac{1}{2}

Now we can compare the two fractions and see that:

12=12 \frac{1}{2}=\frac{1}{2}

Answer

= =

Exercise #6

Choose the appropriate sign:

56?0.9 \frac{5}{6}?0.9

Video Solution

Step-by-Step Solution

First, let's convert 0.9 to a simple fraction.

Since there is only one digit after the decimal point, the number divides by 10 as follows:

0.9=910 0.9=\frac{9}{10}

Now we have two simple fractions with different denominators.

To compare them, note that the smallest common denominator between them is 60.

We'll multiply each one to reach the common denominator as follows:

56×1010=5060 \frac{5}{6}\times\frac{10}{10}=\frac{50}{60}

910×66=5460 \frac{9}{10}\times\frac{6}{6}=\frac{54}{60}

Now we can compare the two fractions and see that:

\frac{50}{60}<\frac{54}{60}

Answer

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Exercise #7

Choose the appropriate sign:

1210?1.2 \frac{12}{10}?1.2

Video Solution

Step-by-Step Solution

First, we will convert the simple fraction to a decimal fraction.

We will write the numerator of the fraction in decimal form and divide by 10 as follows:

12=12.0 12=12.0

12.010=1.2 \frac{12.0}{10}=1.2

Now we can compare the two fractions and see that:

1210=1.2 \frac{12}{10}=1.2

Answer

= =

Exercise #8

Choose the appropriate sign:

58?0.6 \frac{5}{8}?0.6

Video Solution

Step-by-Step Solution

First, let's convert 0.6 to a simple fraction.

Since there is only one digit after the decimal point, the number is divided by 10, therefore:

0.6=610 0.6=\frac{6}{10}

Now we have two simple fractions with different denominators.

Let's find the least common denominator between them, in this case the common denominator is 80.

We'll equate the denominators by multiplying by the appropriate numbers:

58×1010=5080 \frac{5}{8}\times\frac{10}{10}=\frac{50}{80}

610×88=4880 \frac{6}{10}\times\frac{8}{8}=\frac{48}{80}

Now let's compare the numerators and we'll find that:

\frac{50}{80} > \frac{48}{80}

Answer

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Exercise #9

Choose the appropriate sign:

35 [?] 0.5 \frac{3}{5}~[?]~0.5

Video Solution

Step-by-Step Solution

First, let's convert 0.5 to a simple fraction.

Since there is only one digit after the decimal point, the number is divided by 10, therefore:

0.5=510 0.5=\frac{5}{10}

Now we have two simple fractions with different denominators.

Let's find the least common denominator between them, in this case the common denominator is 10.

We'll equate the denominators by multiplying by the appropriate numbers:

35×22=610 \frac{3}{5}\times\frac{2}{2}=\frac{6}{10}

510×11=510 \frac{5}{10}\times\frac{1}{1}=\frac{5}{10}

Now let's compare the numerators and we'll find that:

\frac{6}{10}>\frac{5}{10}

Answer

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Exercise #10

Choose the appropriate sign:

68?0.75 \frac{6}{8}?0.75

Video Solution

Step-by-Step Solution

First, let's convert 0.75 to a simple fraction.

Since there are two numbers after the decimal point, the number is divided by 100, therefore:

0.75=75100 0.75=\frac{75}{100}

Let's reduce the fraction by dividing by 25:

75:25100:25=34 \frac{75:25}{100:25}=\frac{3}{4}

Now we have two simple fractions with different denominators.

Let's find the least common denominator between them, in this case the common denominator is 8.

We'll equate the denominators by multiplying by the appropriate numbers:

68×11=68 \frac{6}{8}\times\frac{1}{1}=\frac{6}{8}

34×22=68 \frac{3}{4}\times\frac{2}{2}=\frac{6}{8}

Now let's compare the numerators and we'll find that:

68=68 \frac{6}{8}=\frac{6}{8}

Answer

= =

Exercise #11

Choose the appropriate sign:

69?0.7 \frac{6}{9}?0.7

Video Solution

Step-by-Step Solution

First, let's convert 0.7 to a simple fraction.

Since there is only one digit after the decimal point, the number divides by 10 as follows:

0.7=710 0.7=\frac{7}{10}

Now we have two simple fractions with different denominators.

In order to compare them, note that the smallest common denominator between them is 90.

We'll multiply each one to reach the common denominator as follows:

69×1010=6090 \frac{6}{9}\times\frac{10}{10}=\frac{60}{90}

710×99=6390 \frac{7}{10}\times\frac{9}{9}=\frac{63}{90}

Now we can compare the two fractions and see that:

\frac{60}{90}<\frac{63}{90}

Answer

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Exercise #12

Choose the appropriate sign:

0.8?8100 0.8?\frac{8}{100}

Video Solution

Step-by-Step Solution

First, let's convert the simple fraction to a decimal fraction.

We'll write the number 8 with two zeros in front of it, and then add the decimal point:

8100=008. \frac{8}{100}=008.

Since the simple fraction is divided by 100, we'll move the decimal point two places to the left and get:

008.=0.08 008.=0.08

Let's compare the two decimal numbers we got, focusing on the number after the decimal point:

0.80 > 0.08

Answer

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Exercise #13

Choose the appropriate sign:

24?0.5 \frac{2}{4}?0.5

Video Solution

Step-by-Step Solution

First, let's convert 0.5 to a simple fraction.

Since there is only one number after the decimal point, the number is divided by 10, therefore:

0.5=510 0.5=\frac{5}{10}

Now we have two simple fractions with different denominators.

Let's find the least common denominator between them, in this case the common denominator is 20.

We'll equalize the denominators by multiplying by the appropriate numbers:

24×55=1020 \frac{2}{4}\times\frac{5}{5}=\frac{10}{20}

510×22=1020 \frac{5}{10}\times\frac{2}{2}=\frac{10}{20}

Now let's compare the numerators and we'll find that:

1020=1020 \frac{10}{20}=\frac{10}{20}

Answer

= =

Exercise #14

Choose the appropriate sign:

15?0.22 \frac{1}{5}?0.22

Video Solution

Step-by-Step Solution

First, let's convert the simple fraction to a decimal fraction.

We'll multiply the fraction so that we get 10 in the denominator:

15×22=210 \frac{1}{5}\times\frac{2}{2}=\frac{2}{10}

Now let's convert the simple fraction we got to a decimal fraction.

Let's write the number 2 as a decimal fraction:

2=2. 2=2.

Since the simple fraction we got is divisible by 10, we'll move the decimal point one place to the left and get:

2.=.2=0.2 2.=.2=0.2

Let's compare the two decimal numbers we got. We'll add 0 to the number 0.2:

0.20 < 0.22

Answer

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