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

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this: