Which of these is the correct expanded form of 6.408?

Class 7Fractions and DecimalsFractions and Decimals

A $6 + \frac{4}{10} + \frac{8}{100}$
B $6 + \frac{4}{100} + \frac{8}{1000}$
C $6 + \frac{4}{10} + \frac{0}{100} + \frac{8}{1000}$
D $6 + \frac{408}{100}$

Step-by-Step Solution

The digits after the point are 4 (tenths), 0 (hundredths) and 8 (thousandths), so

6.408 = 6 + \frac{4}{10} + \frac{0}{100} + \frac{8}{1000}

. The trap is ignoring the zero and sliding the 8 up into hundredths, which gives

6 + \frac{4}{10} + \frac{8}{100}

— that is 6.48, a different number.

Answer: C)

6 + \frac{4}{10} + \frac{0}{100} + \frac{8}{1000}

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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