## Skill Check IV: IITJEE Foundation Maths

I. State whether the following statements are True or False:

(i) 0 is to the left of all negative numbers on the number line.

(ii) 3 is greater than -3333.

(iii) $1\frac{2}{5}$ will lie to the right of the mid-point between 1 and 2 on the number line.

(iv) $1\frac{2}{5}$ will lie to the left of the mid-point between 1 and 2 on the number line.

(v) If a decimal fraction is non-terminating and non-recurring, it is known as a rational number.

(vI) The rational number $3\frac{1}{5}$ lies between $3\frac{2}{11}$ and $3 \frac{3}{11}$

II. How many natural numbers lie between 212 and 2120?

III. How many integers lie between -219 and +2190?

IV. Write the following numbers in descending order: (i) -213, +126, -212, +127, -127 (ii) $-1\frac{7}{11}, -3\frac{7}{11}$, $-2\frac{7}{11}, -5\frac{7}{11}, -4\frac{7}{11}$ (iii) $\frac{3}{5}, -\frac{2}{9}, \frac{5}{7}, -\frac{3}{10}, \frac{11}{21}$ (iv) -2.3838, -2.3388, -2.8838, -2.8833, -2.3883 (v) $3.\overline{8}, 3.\overline{6}, 3.88, 3.6\overline{8}, 3.8\overline{6}$

V. Write the following numbers in ascending order: (i) +418, -481, -418, +481, -841 (II) $-1\frac{3}{11}, -1\frac{4}{11}, -1\frac{5}{11}, -1\frac{6}{11}, -1\frac{7}{11}$ (iii) $\frac{2}{5}, \frac{11}{23}, \frac{7}{15}, \frac{9}{20}, \frac{3}{7}$ (iv) $6.7134, 6.7431, 6.7341, 6.7413, 6.7143$ (v)$7.9\dot{8}, 7.\dot{9}, 7.\overline{98}, 7.8\dot{9}, 7.\dot{8}$

VI. Insert a rational number between the following pairs of numbers: (i) -0.001 and +0.001 (ii) -8 and -3 (iii) 85 and 86 (iv) 5.5 and 6 (v) $\frac{1}{4}$ and $\frac{1}{5}$ (vi) $2\frac{2}{5}, 2\frac{3}{5}$ (vii) 3.0688 and 3.0699 (viii) 5.2168 and 5.2169 (ix) $1\frac{9}{15}, 1\frac{11}{15}$ (x) $-8\frac{6}{7}, -8\frac{5}{7}$

VII. Insert 2 rational numbers between the following numbers: (a) 3.18 and 3.19 (b) $2\frac{2}{5}, 2 \frac{3}{5}$

VIII. Represent the following rational numbers on the number line:

(i) $2\frac{1}{3}$ (ii) $-\frac{5}{7}$ (iii) $3.7$ (iv) $4.85$ (v) $6 \frac{7}{11}$

IX. Which of the following rational numbers will have a terminating decimal value? (a) $\frac{3}{5}$ (b) $-\frac{5}{7}$ (c) $\frac{1}{2}$ (d) $-\frac{7}{10}$ (v) $\frac{7}{15}$

X. Convert each of the following decimal fractions in the form $\frac{p}{q}$, where p and q are both integers, but q is not zero: (a) 0.32 (b) 0.42 (c) 0.85 (d) 1.875 (e) 0.4375 (f) $3.\dot{7}$ (g) $1.6\dot{4}$ (h) $5.\overline{23}$ (i) $7.11\dot{3}$ (j) $8.9\overline{505}$

We will continue this series later…

Regards,

Nalin Pithwa

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