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Dividing a Decimal Fraction by a Decimal Fraction

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■ Rule : Multiply both the dividend and the divisor by a suitable power of 10 to make the divisor a whole number. Now, proceed as above.

e.g. (i) Evaluate : (a) 42 $\div$ .06 (b) .00088 $\div$ .11

Solution.

(a) $\frac{42}{6}$ = 7. ( Difference of decimals = 0 – 2 = – 2 )

So, $\frac{42}{.06}$ = 700 [ = 2 ]

(b) $\frac{88}{11}$ = 8. ( Difference of decimals = 5 – 2 = 3 )

So, $\frac{.00088}{.11}$ = .008 [ = 3 ]

(ii) If 14.528 $\times$ 7.8175 = 113.57264, then find the value of 0.014528 $\times$ 78.175

Soln. In 14.528 $\times$ 7.8175, sum of decimals = 3 + 4 = 7

& in 0.014528 $\times$ 78.175, sum of decimals = 6 + 3 = 9

Now, difference between decimals = new value – old value = 9 – 7 = 2

$\therefore$ 0.014528 78.175 = 1.1357264 [ = 2 ]

(iii) If 55.79019 $\div$ 189.36 = 0.294625, then find the value of 5579.019 $\div$ 0.0018936

Soln. In 55.79019 $\div$ 189.36, difference of decimals = 5 – 2 = 3

& in 5579.019 $\div$ 0.0018936, difference of decimals = 3 – 7 = – 4

Now, difference between decimals = new value – old value = – 4 – 3 = – 7

$\therefore$ 5579.019 $\div$ 0.0018936 = 2946250 [ = 7 ]