Question

Запишите периодические дроби в виде обыкновенных дробей: 0.(3); 0.(7); 0.1(2); 1.12(3); 7.5(4); 0.(12); 1.0(12); 8.7(21)

Answer 1

Решение на фото............

Answer 2

1)0(3)=3/9
2)0,7=7/9
3)0,1(2)=11/90
4)1.12(3)=1, 111/900
5)7,5(4)=7, 50/90
6)0,(12)=12/99
7)1,0(12)=1, 12/90
8)8,7(21)=8, 714/900

Answer 3

Converting Periodic Decimals to Fractions

To convert periodic decimals to fractions, we need to identify the repeating pattern and express it as a fraction. Let's convert the given periodic decimals into fractions:

1. 0.(3): The number 0.(3) represents a repeating decimal where the digit 3 repeats indefinitely. To convert it to a fraction, we can use the following method: - Let x = 0.(3) - Multiply both sides of the equation by 10 to shift the decimal point: 10x = 3.(3) - Subtract the original equation from the shifted equation: 10x - x = 3.(3) - 0.(3) - Simplify: 9x = 3 - Divide both sides by 9: x = 3/9 = 1/3

Therefore, 0.(3) is equal to 1/3.

2. 0.(7): The number 0.(7) represents a repeating decimal where the digit 7 repeats indefinitely. To convert it to a fraction, we can use the same method as above: - Let x = 0.(7) - Multiply both sides of the equation by 10 to shift the decimal point: 10x = 7.(7) - Subtract the original equation from the shifted equation: 10x - x = 7.(7) - 0.(7) - Simplify: 9x = 7 - Divide both sides by 9: x = 7/9

Therefore, 0.(7) is equal to 7/9.

3. 0.1(2): The number 0.1(2) represents a repeating decimal where the digit 2 repeats indefinitely. To convert it to a fraction, we can use a similar method: - Let x = 0.1(2) - Multiply both sides of the equation by 10 to shift the decimal point: 10x = 1.(2) - Subtract the original equation from the shifted equation: 10x - x = 1.(2) - 0.1(2) - Simplify: 9x = 1 - Divide both sides by 9: x = 1/9

Therefore, 0.1(2) is equal to 1/9.

4. 1.12(3): The number 1.12(3) represents a repeating decimal where the digits 1 and 3 repeat indefinitely. To convert it to a fraction, we can use a similar method: - Let x = 1.12(3) - Multiply both sides of the equation by 100 to shift the decimal point: 100x = 112.(3) - Subtract the original equation from the shifted equation: 100x - x = 112.(3) - 1.12(3) - Simplify: 99x = 111 - Divide both sides by 99: x = 111/99

Therefore, 1.12(3) is equal to 37/33.

5. 7.5(4): The number 7.5(4) represents a repeating decimal where the digit 4 repeats indefinitely. To convert it to a fraction, we can use a similar method: - Let x = 7.5(4) - Multiply both sides of the equation by 10 to shift the decimal point: 10x = 75.(4) - Subtract the original equation from the shifted equation: 10x - x = 75.(4) - 7.5(4) - Simplify: 9x = 68 - Divide both sides by 9: x = 68/9

Therefore, 7.5(4) is equal to 68/9.

6. 0.(12): The number 0.(12) represents a repeating decimal where the digits 1 and 2 repeat indefinitely. To convert it to a fraction, we can use a similar method: - Let x = 0.(12) - Multiply both sides of the equation by 100 to shift the decimal point: 100x = 12.(12) - Subtract the original equation from the shifted equation: 100x - x = 12.(12) - 0.(12) - Simplify: 99x = 12 - Divide both sides by 99: x = 12/99

Therefore, 0.(12) is equal to 4/33.

7. 1.0(12): The number 1.0(12) represents a repeating decimal where the digits 1 and 2 repeat indefinitely. To convert it to a fraction, we can use a similar method: - Let x = 1.0(12) - Multiply both sides of the equation by 10 to shift the decimal point: 10x = 10.(12) - Subtract the original equation from the shifted equation: 10x - x = 10.(12) - 1.0(12) - Simplify: 9x = 9 - Divide both sides by 9: x = 1

Therefore, 1.0(12) is equal to 1.

8. 8.7(21): The number 8.7(21) represents a repeating decimal where the digits 2 and 1 repeat indefinitely. To convert it to a fraction, we can use a similar method: - Let x = 8.7(21) - Multiply both sides of the equation by 100 to shift the decimal point: 100x = 871.(21) - Subtract the original equation from the shifted equation: 100x - x = 871.(21) - 8.7(21) - Simplify: 99x = 862 - Divide both sides by 99: x = 862/99

Therefore, 8.7(21) is equal to 862/99.

Please let me know if you have any further questions!