Write 5/3 as a Decimal
The Correct Answer and Explanation is:
Correct Answer:53=1.666…=1.6‾\frac{5}{3} = 1.666\ldots = 1.\overline{6}35=1.666…=1.6
Explanation:
To convert the fraction 53\frac{5}{3}35 to a decimal, divide the numerator (5) by the denominator (3). Begin by setting up the division:5÷35 \div 35÷3
Three goes into five one time. Multiply:1×3=31 \times 3 = 31×3=3
Subtract:5−3=25 – 3 = 25−3=2
Since 2 is less than 3 and the division is not complete, add a decimal point and bring down a zero. Now divide 20 by 3:20÷3=620 \div 3 = 620÷3=6
Multiply:6×3=186 \times 3 = 186×3=18
Subtract:20−18=220 – 18 = 220−18=2
Again, bring down a zero. The same steps repeat:20÷3=6,6×3=18,20−18=220 \div 3 = 6, \quad 6 \times 3 = 18, \quad 20 – 18 = 220÷3=6,6×3=18,20−18=2
This process continues indefinitely, with 6 repeating over and over. So, the decimal representation is:1.666…1.666\ldots1.666…
The 6 repeats without end, so use a bar notation to show that the 6 is repeating:53=1.6‾\frac{5}{3} = 1.\overline{6}35=1.6
This type of decimal is called a repeating decimal. A repeating decimal has one or more digits that repeat forever. In this case, only one digit (6) repeats.
Fractions where the denominator is not a factor of a power of 10 often result in repeating decimals. Since 3 is not a factor of 10 or any power of 10 like 100 or 1000, the division does not terminate. Instead, it cycles in a repeating pattern.
Understanding how to convert fractions to decimals is an essential math skill, especially when comparing values, estimating, or solving problems involving money or measurements.
