Decimal Fractions — Mental Maths

Fill in the blanks:

(i) 6 hundredths in decimal form is ............... .

(ii) $\dfrac{6}{25}$ in decimal form is ............... .

(iii) 2 m 15 cm + 6 m 5 cm = ............... metres.

(iv) 15P + 5P = ₹ ............... .

(v) 15 km + 75 m = ............... .

(vi) (2 cm - 5 mm) = ............... cm.

Answer

(i) 6 hundredths is represented as $\dfrac{6}{100}$

So, $\dfrac{6}{100}=0.06$

6 hundredths in decimal form is 0.06.

(ii) We have,

$\dfrac{6}{25} = \dfrac{6 \times 4}{25 \times 4} = \dfrac{24}{100} = 0.24$

$\dfrac{6}{25}$ in decimal form is 0.24.

(iii) We know that,

2 m 15 cm = 2 m + $\dfrac{15}{100}$ = 2 m + 0.15 = 2.15 m

6 m 5 cm = 6 m + $\dfrac{5}{100}$ = 6 m + 0.05 = 6.05 m

Writing in column form and adding:

$\begin{array}{r} \phantom{+}2.15 \\ +\space 6.05 \\ \hline 8.20 \end{array}$

2 m 15 cm + 6 m 5 cm = 8.20 metres.

(iv) We have,

15 P = $\dfrac{15}{100} = ₹ 0.15$

5 P = $\dfrac{5}{100} = ₹ 0.05$

Writing in column form and adding:

$\begin{array}{r} \phantom{+}0.15 \\ +\space 0.05 \\ \hline 0.20 \end{array}$

So, 15 P + 5 P = ₹ ( 0.15 + 0.05 ) = ₹ 0.20.

(v) We know that, 75 m = $\dfrac{75}{1000}$ km = 0.075 km.

15 km + 75 m = ( 15.000 + 0.075 ) km

Writing in column form and adding:

$\begin{array}{r} \phantom{+}15.000 \\ +\space 0.075 \\ \hline 15.075 \end{array}$

So, 15 km + 75 m = 15.075 km.

(vi) We have, 5 mm = $\dfrac{5}{10}$ cm = 0.5 cm.

(2 cm - 5 mm) = (2.0 - 0.5) cm

Writing in column form and subtracting:

$\begin{array}{r} \phantom{+}2.0 \\ -\space 0.5 \\ \hline 1.5 \end{array}$

So, (2 cm - 5 mm) = 1.5 cm.

Write (T) for true and (F) for false for each of the statements given below:

(i) 3 m 5 cm = 3.5 m

(ii) 16 km 30 m = 16.30 km

(iii) ₹ 8 + 6 P = ₹ (8.60)

(iv) 0.03 = 3 hundredths

(v) 7 kg 80 g = 7.8 kg

(vi) 0.1 + 0.01 + 0.001 = 0.111

Answer

(i) F

Reason —

3 m 5 cm = 3 m + $\dfrac{5}{100}$ m = 3 m + 0.05 m = 3.05 m, and not 3.5 m.

(ii) F

Reason —

16 km 30 m = 16 km + $\dfrac{30}{1000}$ km = 16 km + 0.030 km = 16.030 km, not 16.30 km.

(iii) F

Reason — Here, 6 P = $\dfrac{6}{100} ₹= ₹ 0.06$.

So, ₹ 8 + 6 P = ₹ (8 + 0.06) = ₹ 8.06.

(iv) T

Reason —

0.03 = $\dfrac{3}{100}$

So, 0.03 is 3 hundredths.

(v) F

Reason — We have, 80 g = $\dfrac{80}{1000}$ kg = 0.08 kg.

So, 7 kg 80 g =(7 + 0.08) kg = 7.08 kg

(vi) T

Reason — Rewriting the decimals to be like decimals,

0.1 + 0.01 + 0.001 = 0.100 + 0.010 + 0.001

Writing in column form and adding:

$\begin{array}{r} \phantom{+}0.100 \\ 0.010 \\ +\space 0.001 \\ \hline 0.111 \end{array}$

So the sum is 0.111.