Reduction and Expansion of Decimal Fractions: Reducing the fraction

Examples with solutions for Reduction and Expansion of Decimal Fractions: Reducing the fraction

Exercise #1

Reduce the following fraction:

0.25 0.25

Step-by-Step Solution

To reduce the fraction 0.25 0.25 , we note that it is already in its simplest form as a decimal fraction and cannot be reduced further. Therefore, the reduced form is 0.25 0.25 itself.

Answer

0.25 0.25

Exercise #2

Reduce the following fraction:

0.40 0.40

Step-by-Step Solution

To reduce the fraction 0.40 0.40 , we recognize that trailing zeros in decimals do not affect their value. Thus, we can remove the zero to obtain 0.4 0.4 . Therefore, 0.40=0.4 0.40 = 0.4 .

Answer

0.4 0.4

Exercise #3

Reduce the following fraction:

0.50 0.50

Step-by-Step Solution

To reduce the fraction 0.50 0.50 , you need to express it in its simplest form by removing any trailing zeros. The trailing zero in 0.50 0.50 doesn't change the value of the number, as it represents tenths. Without the zero, the number is reduced to 0.5 0.5 , which is the simplest form.

Answer

0.5 0.5

Exercise #4

Reduce the following fraction:

0.56000 0.56000

Step-by-Step Solution

To reduce the decimal fraction 0.56000 0.56000 , we eliminate trailing zeros that have no significance after the decimal point. Thus, 0.56000 0.56000 becomes 0.56 0.56 .
Therefore, the reduced fraction is 0.56 0.56 .

Answer

0.56 0.56

Exercise #5

Reduce the following fraction:

0.5 0.5

Step-by-Step Solution

To reduce 0.5 0.5 , recognize that it's already in its simplest form as a decimal fraction.

When expressed as a fraction of 1, 0.5 0.5 is equivalent to 12 \frac{1}{2} , which means 0.5 0.5 is simplified.

Answer

0.5 0.5

Exercise #6

Reduce the following fraction:

0.600 0.600

Step-by-Step Solution

To reduce the fraction 0.600 0.600 , we look to express it in its simplest form. By removing trailing zeros, we arrive at 0.6 0.6 , which is the same value and represents the simplest form of the number. The trailing zeros in a decimal do not affect its value.

Answer

0.6 0.6

Exercise #7

Reduce the following fraction:

0.7000 0.7000

Step-by-Step Solution

If you have a fraction like 0.7000 0.7000 , you can simplify it by removing all the trailing zeros. Thus, it reduces down to 0.7 0.7 . All the trailing zeros to the right of the decimal point in a number can be eliminated without changing the value of the number.

Answer

0.7 0.7

Exercise #8

Reduce the following fraction:

0.75 0.75

Step-by-Step Solution

To reduce 0.75 0.75 , notice that it represents 75100 \frac{75}{100} .

The greatest common divisor of 75 and 100 is 25, so divide both the numerator and the denominator by 25.

This reduces the fraction to 34 \frac{3}{4} , which is 0.75 0.75 when expressed as a decimal.

Answer

0.75 0.75

Exercise #9

Reduce the following fraction:

0.8400 0.8400

Step-by-Step Solution

To reduce the decimal fraction 0.8400 0.8400 , we eliminate the trailing zeros. Thus, 0.8400 0.8400 becomes 0.84 0.84 . As a result, the reduced fraction is 0.84 0.84 .

Answer

0.84 0.84

Exercise #10

Reduce the following fraction:

0.99000 0.99000

Step-by-Step Solution

To reduce the decimal fraction 0.99000 0.99000 , trailing zeros are removed. Therefore, 0.99000 0.99000 simplifies to 0.99 0.99 . Hence, the reduced fraction is 0.99 0.99 .

Answer

0.99 0.99

Exercise #11

Reduce the following decimal:

0.375 0.375

Step-by-Step Solution

To reduce the decimal 0.375 0.375 , observe that 0.375 0.375 is already a properly expressed finite decimal fraction. Reducing would imply expressing it in another form but since 0.375 0.375 cannot be simplified further while maintaining its value, it's already in its simplest form. The fraction remains 0.375 0.375 .

Answer

0.375 0.375

Exercise #12

Reduce the following fraction:

0.003050 0.003050

Step-by-Step Solution

To reduce 0.003050 0.003050 , remove any trailing zero, resulting in 0.00305 0.00305 .

Answer

0.00305 0.00305

Exercise #13

Reduce the following fraction:

0.10200 0.10200

Step-by-Step Solution

To simplify 0.10200 0.10200 , remove all trailing zeroes, which gives 0.102 0.102 .

Answer

0.102 0.102

Exercise #14

Reduce the following fraction:

0.2040 0.2040

Step-by-Step Solution

To reduce 0.2040 0.2040 , remove any trailing zeroes in the decimal. Therefore, 0.2040 0.2040 simplifies to 0.204 0.204 .

Answer

0.204 0.204

Exercise #15

Reduce the following fraction:

0.256 0.256

Step-by-Step Solution

To reduce the decimal 0.256 0.256 , note that reducing a decimal fraction means simply to write it as a fraction if possible. However, 0.256 0.256 is already in its lowest terms as it's a simple decimal representation without repeating digits and without opportunity to reduce it further. Thus, the fraction 0.256 0.256 cannot be reduced further.

Answer

0.256 0.256

Exercise #16

Reduce the following fraction:

0.3070 0.3070

Step-by-Step Solution

The fraction 0.3070 0.3070 can be reduced by removing the trailing zero since trailing zeros do not affect the value of the number. Therefore, we have:

0.3070=0.307 0.3070 = 0.307

Answer

0.307 0.307

Exercise #17

Reduce the following fraction:

0.4500 0.4500

Step-by-Step Solution

To reduce 0.4500 0.4500 , remove any trailing zeroes. Thus, 0.4500 0.4500 becomes 0.45 0.45 .

Answer

0.45 0.45

Exercise #18

Reduce the following fraction:

0.5005 0.5005

Step-by-Step Solution

The fraction 0.5005 0.5005 cannot be further reduced by removing zeros since the final zero is between non-zero digits. So, the fraction remains:

0.5005 0.5005

Answer

0.5005 0.5005

Exercise #19

Reduce the following fraction:

0.6200 0.6200

Step-by-Step Solution

The fraction 0.6200 0.6200 can be reduced by removing trailing zeros since they do not affect the value. Therefore, it becomes:

0.62 0.62

Answer

0.62 0.62