CBSE Class 5 Mathematics Hindu Arabic Numerals Worksheet

1. Write the Roman numeral for the following Hindu-Arabic numerals.
a) 78: LXXVIII
b) 55: LV
c) 121: CXXI
d) 345: CCCXLV
e) 298: CCXCVIII
f) 449: CDXLIX
g) 190: CXC
h) 210: CCX
i) 320: CCCXX
j) 83: LXXXIII
Answer:
a) \(78 = 70 + 8 = \text{LXX} + \text{VIII} = \text{LXXVIII}\)
b) \(55 = 50 + 5 = \text{L} + \text{V} = \text{LV}\)
c) \(121 = 100 + 20 + 1 = \text{C} + \text{XX} + \text{I} = \text{CXXI}\)
d) \(345 = 300 + 40 + 5 = \text{CCC} + \text{XL} + \text{V} = \text{CCCXLV}\)
e) \(298 = 200 + 90 + 8 = \text{CC} + \text{XC} + \text{VIII} = \text{CCXCVIII}\)
f) \(449 = 400 + 40 + 9 = \text{CD} + \text{XL} + \text{IX} = \text{CDXLIX}\)
g) \(190 = 100 + 90 = \text{C} + \text{XC} = \text{CXC}\)
h) \(210 = 200 + 10 = \text{CC} + \text{X} = \text{CCX}\)
i) \(320 = 300 + 20 = \text{CCC} + \text{XX} = \text{CCCXX}\)
j) \(83 = 50 + 30 + 3 = \text{L} + \text{XXX} + \text{III} = \text{LXXXIII}\)
In simple words: Break each number into hundreds, tens, and ones, then write their Roman equivalents.

Exam Tip: Remember standard Roman values: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500.

2. Write the Hindu-Arabic numeral for the following Roman numerals.
a) LXX = 70
b) XIV = 14
c) CXCV = 195
d) CDX = 410
e) CCIX = 209
f) CLXIX = 169
g) CDXXVII = 427
h) CCCLXXV = 375
i) DVIII = 508
j) XCVI = 96
Answer:
a) \(\text{LXX} = 50 + 20 = 70\)
b) \(\text{XIV} = 10 + 4 = 14\)
c) \(\text{CXCV} = 100 + 90 + 5 = 195\)
d) \(\text{CDX} = 400 + 10 = 410\)
e) \(\text{CCIX} = 200 + 9 = 209\)
f) \(\text{CLXIX} = 100 + 50 + 10 + 9 = 169\)
g) \(\text{CDXXVII} = 400 + 20 + 7 = 427\)
h) \(\text{CCCLXXV} = 300 + 50 + 20 + 5 = 375\)
i) \(\text{DVIII} = 500 + 8 = 508\)
j) \(\text{XCVI} = 90 + 6 = 96\)
In simple words: Add the values of symbols, keeping in mind that a smaller symbol before a larger one means subtraction.

Exam Tip: When a smaller letter appears before a larger letter, subtract its value (e.g., XC = 100 - 10 = 90).

3. Mention which of the following are meaningless; otherwise write the corresponding Hindu-Arabic numeral.
a) IC = Meaningless
b) CI = 101
c) LD = Meaningless
d) CD = 400
e) DD = Meaningless
f) CCCLIX = 359
g) CCCVII = 307
h) CXXXXV = Meaningless
i) LLX = Meaningless
j) VD = Meaningless
Answer:
a) IC: Meaningless (I can only be subtracted from V and X, not C)
b) \(\text{CI} = 100 + 1 = 101\)
c) LD: Meaningless (L, D, and V are never subtracted)
d) \(\text{CD} = 500 - 100 = 400\)
e) DD: Meaningless (D, L, and V are never repeated)
f) \(\text{CCCLIX} = 300 + 50 + 9 = 359\)
g) \(\text{CCCVII} = 300 + 7 = 307\)
h) CXXXXV: Meaningless (X cannot be repeated 4 times consecutively)
i) LLX: Meaningless (L cannot be repeated)
j) VD: Meaningless (V cannot be subtracted)
In simple words: Check Roman numeral rules: symbols V, L, D are never repeated and never subtracted, and a symbol cannot be repeated more than three times.

Exam Tip: Memorize the basic rules: V, L, and D are never subtracted; X can be subtracted from L and C only; C can be subtracted from D and M only.

4. Insert the appropriate symbol >, < or =.
a) XLIII [ ] LXIV
b) CXLIX [ ] CLXXXIX
c) XCVI [ ] LXVI
d) CDLII [ ] CDLIII
Answer:
a) XLIII (43) < LXIV (64)
b) CXLIX (149) < CLXXXIX (189)
c) XCVI (96) > LXVI (66)
d) CDLII (452) < CDLIII (453)
In simple words: Convert both Roman numerals to Hindu-Arabic numbers first, then compare them.

Exam Tip: Always evaluate both sides into standard numbers to avoid comparison mistakes.

5. Arrange the following Roman numerals in ascending order.
a) XXXIII, XLII, LV, LIX
b) XCV, XCII, CIX, CI
c) CCCIX, CCCXX, CCCVIII, CCXL
Answer:
a) XXXIII, XLII, LV, LIX
(Values: 33, 42, 55, 59 - already in ascending order)
b) XCV, XCII, CIX, CI
(Values: 95, 92, 109, 101)
Ascending order: XCII, XCV, CI, CIX
c) CCCIX, CCCXX, CCCVIII, CCXL
(Values: 309, 320, 308, 240)
Ascending order: CCXL, CCCVIII, CCCIX, CCCXX
In simple words: Convert all given Roman numerals into numbers, sort them from smallest to largest, and write back their Roman forms.

Exam Tip: Ascending order means arranging from smallest to largest.

1. Which is greater?
a) 0.3 or 0.003
b) 0.7 or 0.4
c) 0.2 or 0.22
d) 1.045 or 1.5
e) 2.996 or 2.3
f) 4.7 or 4.61
g) 0.1 or 0.0001
h) 0.9 or 0.99
Answer:
a) 0.3 (since 0.300 > 0.003)
b) 0.7 (since 7/10 > 4/10)
c) 0.22 (since 0.20 < 0.22)
d) 1.5 (since 1.500 > 1.045)
e) 2.996 (since 2.996 > 2.300)
f) 4.7 (since 4.70 > 4.61)
g) 0.1 (since 0.1000 > 0.0001)
h) 0.99 (since 0.90 < 0.99)
In simple words: Equalize the number of decimal places by adding trailing zeros, then compare the numbers.

Exam Tip: Compare digits from left to right starting from the tenths place.

2. Express as rupees using decimals.
a) 8p
b) Rs. 2 20p
c) Rs. 82 50p
d) 460p
e) Rs. 7 50p
Answer:
a) 8p = Rs. \(\frac{8}{100}\) = Rs. 0.08
b) Rs. 2 20p = Rs. \(2 + \frac{20}{100}\) = Rs. 2.20
c) Rs. 82 50p = Rs. \(82 + \frac{50}{100}\) = Rs. 82.50
d) 460p = Rs. \(\frac{460}{100}\) = Rs. 4.60
e) Rs. 7 50p = Rs. \(7 + \frac{50}{100}\) = Rs. 7.50
In simple words: Divide paise by 100 to convert into rupees.

Exam Tip: 1 rupee = 100 paise, so divide by 100 or shift the decimal point two places to the left.

3. Express.
a) 2 cm in m and km
b) 25 cm in m and km
c) 35 mm in cm and km
d) 400 gm in km
e) 2560 gm in kg
Answer:
a) 2 cm = \(\frac{2}{100}\) m = 0.02 m
2 cm = \(\frac{2}{100000}\) km = 0.00002 km
b) 25 cm = \(\frac{25}{100}\) m = 0.25 m
25 cm = \(\frac{25}{100000}\) km = 0.00025 km
c) 35 mm = \(\frac{35}{10}\) cm = 3.5 cm
35 mm = \(\frac{35}{1000000}\) km = 0.000035 km
d) 400 gm = \(\frac{400}{1000000}\) kg = 0.0004 kg (Note: km for grams is a unit conversion context issue in standard measures, expressed here as fraction of metric ton or standard mass unit relative to km scale, strictly converting 400 gm = 0.4 kg = 0.0004 tonnes)
e) 2560 gm = \(\frac{2560}{1000}\) kg = 2.56 kg
In simple words: Use conversion factors: 1 m = 100 cm, 1 km = 1000 m, 1 kg = 1000 g, 1 cm = 10 mm.

Exam Tip: Moving from smaller units to larger units requires division.

4. Solve and match the integers in column 1 with column 2.
Answer:
Let us solve each expression in Column 1 and Column 2 to find the correct matches:
Column 1:
a) \((-6) \times (10) = -60\)
b) \((+12) \times (-6) = -72\)
c) \((-8) \times (-8) = +64\)
d) \((+11) \times (-19) = -209\)
e) \((-12) \times (-16) = +192\)
f) \((+9) \times (+12) = +108\)
g) \((-9) \times (-9) = +81\)
h) \((-13) \times (-7) = +91\)
i) \((-12) \times (11) = -132\)
j) \((-14) \times (+8) = -112\)
k) \((+13) \times (-9) = -117\)
l) \((-15) \times (-8) = +120\)
m) \((+3) \times (-15) = -45\)
n) \((+6) \times (+8) = +48\)
o) \((+9) \times (0) = 0\)
p) \((+6) \times (-5) = -30\)

Column 2:
i) \((-24) \times (-8) = +192\) (Matches e)
ii) \((-9) \times (+5) = -45\) (Matches m)
iii) \((-12) \times (-4) = +48\) (Matches n)
iv) \((+18) \times (+6) = +108\) (Matches f)
v) \((-39) \times (+3) = -117\) (Matches k)
vi) \((-27) \times (-3) = +81\) (Matches g)
vii) \((+2) \times (0) = 0\) (Matches o)
viii) \((+15) \times (-4) = -60\) (Matches a)
ix) \((+6) \times (-22) = -132\) (Matches i)
x) \((+7) \times (+13) = +91\) (Matches h)
xi) \((-4) \times (+28) = -112\) (Matches j)
xii) \((-9) \times (+8) = -72\) (Matches b)
xiii) \((12) \times (10) = +120\) (Matches l)
xiv) \((-15) \times (+2) = -30\) (Matches p)
xv) \((+16) \times (4) = +64\) (Matches c)
xvi) \((+209) \times (-1) = -209\) (Matches d)

Final Matching Pairs:
a - viii, b - xii, c - xv, d - xvi, e - i, f - iv, g - vi, h - x, i - ix, j - xi, k - v, l - xiii, m - ii, n - iii, o - vii, p - xiv
In simple words: Multiply each pair of integers considering sign rules: (+) \times (+) = (+), (-) \times (-) = (+), and (+) \times (-) = (-).

Exam Tip: Product of two negative integers is always positive, and product of a positive and a negative integer is always negative.