Which of these decimals is the greatest: 0.4, 0.39, 0.409 or 0.4009?

Class 7Fractions and DecimalsFractions and Decimals

A0.4009
B0.4
C0.39
D0.409

Step-by-Step Solution

Give them all the same number of decimal places: 0.4000, 0.3900, 0.4090, 0.4009. Comparing left to right, 0.4090 is the largest. The trap is thinking more digits means a bigger number, which points to 0.4009.

Answer: D) 0.409

Key idea: Dividing fractions: multiply by the reciprocal

Dividing by a fraction is the **same as multiplying by its reciprocal**. To divide, flip the second fraction (the divisor) and multiply.

(a/b) ÷ (c/d) = (a/b) × (d/c) = (a × d) / (b × c).

Example: (2/3) ÷ (4/5) = (2/3) × (5/4) = 10/12 = 5/6.

Why? Dividing by 1/4 is the same as asking 'how many quarters fit in this?' — which is the same as multiplying by 4. The reciprocal trick generalises that idea.

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