Decimals — conversion, operations, and comparison with fractions

Question

(a) Convert $\dfrac{3}{8}$ to a decimal. (b) Arrange in ascending order: $0.5$ , $\dfrac{3}{8}$ , $0.42$ . (c) Find $2.35 + 0.8 - 1.157$ .

(CBSE Class 6 pattern)

Solution — Step by Step

Divide 3 by 8:

$3 \div 8 = 0.375$

So $\dfrac{3}{8} = 0.375$ .

Quick check: $0.375 \times 8 = 3$ ✓

We have: $0.5$ , $0.375$ , $0.42$ .

To compare, make all decimals have the same number of digits: $0.500$ , $0.375$ , $0.420$ .

Ascending order: $0.375 < 0.420 < 0.500$

So: $\mathbf{\dfrac{3}{8} < 0.42 < 0.5}$

Align the decimal points and add zeros where needed:

2.350 + 0.800 = 3.150

3.150 - 1.157 = \mathbf{1.993}

Always line up the decimal points vertically — this prevents place value errors.

flowchart TD
    A["Fraction to Decimal"] --> B["Divide numerator by denominator"]
    B --> C["3 ÷ 8 = 0.375"]
    D["Comparing decimals"] --> E["Convert all to same form"]
    E --> F["Make equal decimal places"]
    F --> G["Compare digit by digit from left"]
    H["Decimal arithmetic"] --> I["Align decimal points"]
    I --> J["Add zeros to match lengths"]
    J --> K["Add/subtract normally"]

Why This Works

Decimals and fractions are two ways to write the same number. Every fraction can be written as a decimal (by dividing), and every terminating decimal can be written as a fraction.

$0.375 = \dfrac{375}{1000} = \dfrac{3}{8}$ (after simplifying by dividing both by 125).

When comparing, converting to the same form (all decimals or all fractions with the same denominator) makes the comparison straightforward. With decimals, we compare digit by digit from left to right, just like comparing whole numbers after aligning the decimal point.

Alternative Method — Convert Everything to Fractions

Instead of decimals, convert to fractions with a common denominator:

$0.5 = \dfrac{1}{2} = \dfrac{20}{40}$ , $\dfrac{3}{8} = \dfrac{15}{40}$ , $0.42 = \dfrac{42}{100} = \dfrac{21}{50} = \dfrac{16.8}{40}$

Since $15 < 16.8 < 20$ , the order is $\dfrac{3}{8} < 0.42 < 0.5$ .

For quick conversion of common fractions: $\dfrac{1}{8} = 0.125$ , $\dfrac{1}{4} = 0.25$ , $\dfrac{3}{8} = 0.375$ , $\dfrac{1}{2} = 0.5$ , $\dfrac{5}{8} = 0.625$ , $\dfrac{3}{4} = 0.75$ . Memorising the eighths family saves time in MCQ exams.

Common Mistake

Students often think $0.42 > 0.5$ because “42 is bigger than 5.” This is wrong because they are comparing as if these are whole numbers. In decimals, the first digit after the decimal point (tenths) matters most. $0.5 = 0.50$ , and $50 > 42$ , so $0.5 > 0.42$ . Always equalize the number of decimal places before comparing.

Question

Solution — Step by Step

Why This Works

Alternative Method — Convert Everything to Fractions

Common Mistake

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