Convert 3/8 to decimal and percentage

Question

Convert the fraction $\frac{3}{8}$ into (a) a decimal and (b) a percentage.

(NCERT Class 6)

Solution — Step by Step

Divide the numerator by the denominator:

\frac{3}{8} = 3 \div 8

Performing the long division: $8$ goes into $30$ three times ( $24$ ), remainder $6$ . Bring down $0$ : $8$ goes into $60$ seven times ( $56$ ), remainder $4$ . Bring down $0$ : $8$ goes into $40$ five times ( $40$ ), remainder $0$ .

\frac{3}{8} = \mathbf{0.375}

To convert a decimal to a percentage, multiply by 100:

0.375 \times 100 = \mathbf{37.5\%}

So $\frac{3}{8} = 0.375 = 37.5\%$ .

Why This Works

A fraction represents division. When we divide 3 by 8, we get the decimal form. A percentage literally means “per hundred” — so multiplying by 100 tells us how many parts out of 100 the fraction represents.

We can verify: $37.5\%$ of $8 = \frac{37.5}{100} \times 8 = 3$ . This confirms our answer.

Alternative Method — Make the Denominator 1000

\frac{3}{8} = \frac{3 \times 125}{8 \times 125} = \frac{375}{1000} = 0.375

We multiplied by 125 because $8 \times 125 = 1000$ . This avoids long division.

For the percentage: $\frac{3}{8} = \frac{3 \times 12.5}{8 \times 12.5} = \frac{37.5}{100} = 37.5\%$ .

Some fractions are worth memorising as decimals: $\frac{1}{8} = 0.125$ , $\frac{1}{4} = 0.25$ , $\frac{3}{8} = 0.375$ , $\frac{1}{2} = 0.5$ , $\frac{5}{8} = 0.625$ , $\frac{3}{4} = 0.75$ , $\frac{7}{8} = 0.875$ . These come up often in exams and speed up calculations.

Common Mistake

When dividing 3 by 8, students sometimes write 3/8 = 2.66… (confusing it with 8/3). Always check: the fraction $\frac{3}{8}$ is less than 1 (numerator is smaller than denominator), so the decimal must be less than 1. If you get a number greater than 1, you have divided the wrong way around.

Question

Solution — Step by Step

Why This Works

Alternative Method — Make the Denominator 1000

Common Mistake

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