Page 29 - Start Up Mathematics_6

Remarks:

• V, L and D are never subtracted from a symbol of larger value.
• I can be subtracted from V and X only.

• X can be subtracted from L and C only.
• C can be subtracted from D and M only.

Rule 4: When a symbol of smaller value is written between two symbols of larger values, it is
always subtracted from the symbol of larger value, which comes immediately after the
symbol of smaller value.

Examples:
 XIX = 10 + (10 – 1) = 19  CXIV = 100 + 10 + (5 – 1) = 114
 CLIV = 100 + 50 + (5 – 1) = 154  CCIX = 100 + 100 + (10 – 1) = 209
Rule 5: If a bar is placed over a symbol, its value gets multiplied by 1,000.
Examples:

 V = 5 × 1,000 = 5,000  L = 50 × 1,000 = 50,000

EXERCISE 1.4

1. Simplify:
(a) 7 × (11+ 9) (b) 42 + (73 – 23) (c) 248 – (300 – 152)
(d) (27 + 23) (68 – 58) (e) 287 × 90 (f) 105 × 95

2. Write the equivalent Roman numerals for the following Hindu-Arabic numerals:
(a) 22 (b) 28 (c) 32 (d) 45 (e) 47
(f) 55 (g) 64 (h) 81 (i) 93 (j) 97
(k) 326 (l) 548 (m) 991 (n) 1,207 (o) 3,919
3. Express each of the following in Hindu-Arabic numerals:
(a) XVII (b) XXIV (c) XLV (d) LI (e) XCII

(f) XCV (g) CLXXXVII (h) CCCLXXXIII (i) CDXLIX (j) MCDLV
(k) MDCCXXV (l) MMMDXXI

At a Glance

1. The process of writing a number in digits is called notation and the process of writing a
number in words is called numeration.

2. In the Indian system of numeration commas are placed after 3 digits starting from the right.
The other periods to the left of the ones period have two places each.

3. In the International system of numeration commas are placed after every 3 digits from the
right.

4. The face value of a digit is the number or a symbol it represents irrespective of its position
in the number.

5. The place value of a digit in a number is its face value multiplied by its position value. The
place value of a digit is the value of the digit because of its position in the number.

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