This method is useful when we have to multiply two numbers which are near the base numbers like 10, 100, and other powers of 10. First let us learn how to handle numbers lower than a particular base.
Example: 95 x 98, where both numbers are less than 100, taking 100 as the base.
Let us look at the steps for solving the problem.
95 is 5 less than 100 and 98 is 2 less than 100.
Step 1: 95 – 2 = 93
98 – 5 = 93
Step 2: Multiply 5 x 2 = 10
Step 3: The answer is 9310
95 x 98 = 9310
Example: 91 x 92
91 is 9 less than 100 and 92 is 8 less than 100.
Step 1: 91 – 8 = 83
92 – 9 = 83
Step 2: Multiply 9 x 8 = 72
Step 3: The answer is 8372
91 x 92 = 8372
Example: 98 x 97
98 is 2 less than 100 and 97 is 3 less than 100.
Step 1: 98 – 3 = 95
97 – 2 = 95
Step 2: Multiply 3 x 2 = 6
Since the base is 100 we need to have 2 digits so take 6 as 06
Step 3: The answer is 9506
98 x 97 = 9506
World’s Great Mathematicians.
Archimedes (287 – 212 B C)
Archimedes was a famous Greek mathematician and physicist. He was born in 287 BC at Syracuse, Sicily.
Today when we get an idea, we often shout the word ‘Eureka’. This famous word is originally attributed to Archimedes, who supposedly shouted it when he discovered how to measure the volume of an object with an irregular shape. When King Hiero ordered a gold crown, he suspected that it was not made of pure gold but had silver in it. However, he could not prove this. He told Archimedes of his suspicion. And Archimedes’s thoughts revolved around the problem, One day when he lay in his bathtub, he realised that the volume of water that overflowed from the tub was proportional to how much of his body was submerged. At the realisation he ran out on to the streets of Syracuse, completely naked, shouting “Eureka”.
This principle is known as the ‘Archimedes Principle’. But the example of the golden crown does not appear in any known work of Archimedes.
Archimedes gave a remarkably accurate approximation of pi. He also proved that the area of a circle was equal to pi multiplied by the square of the radius of the circle. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series. Archimedes is known to have invented his own Greek number system, so that he could accommodate more of his invented numbers. His greatest works are Integral Calculus, Measurement of Circle and The Quadrature of the Parabola.
He designed several war machines worked by means of levers and pulleys. He studied the properties of light with the help of mirrors.