The ratio 4:9 equals which repeating decimal?

The ratio 4:9 equals which repeating decimal?

• A. 0.333... (repeating)
• B. 0.444... (repeating)
• C. 0.222... (repeating)
• D. 0.666... (repeating)

Answer: (B)

Converting a ratio to a decimal uses the fraction form. The ratio 4:9 is 4/9. Repeating decimals come from dividing by 9: 1/9 is 0.111..., so multiplying by 4 gives 4/9 = 0.444... The long-division view matches this: 4 divided by 9 gives 0 with a remainder of 4, bringing down zeros keeps yielding 4 as the next digit, repeating forever. This pattern shows why the decimal for four ninths is 0.444... The other repeating decimals correspond to different fractions (for example, 1/3 is 0.333..., 2/3 is 0.666...), so they don’t match 4/9.

Converting a ratio to a decimal uses the fraction form. The ratio 4:9 is 4/9. Repeating decimals come from dividing by 9: 1/9 is 0.111..., so multiplying by 4 gives 4/9 = 0.444... The long-division view matches this: 4 divided by 9 gives 0 with a remainder of 4, bringing down zeros keeps yielding 4 as the next digit, repeating forever. This pattern shows why the decimal for four ninths is 0.444... The other repeating decimals correspond to different fractions (for example, 1/3 is 0.333..., 2/3 is 0.666...), so they don’t match 4/9.