Find the product of 105- 101- 102

The product #160; 105× 101× 102 can be rewritten as #160; (100+5)× (100+1)× (100+2) .Firstly multiply the first and second term as follows: (10 ...

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Standard VI

Mathematics

Introducing Large Numbers

Find the prod...

Question

Find the product of $105 \times 101 \times 102$

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Solution

The product $105 \times 101 \times 102$ can be rewritten as $(100 + 5) \times (100 + 1) \times (100 + 2)$ .

Firstly multiply the first and second term as follows:

$(100 + 5) (100 + 1) (100 + 2) = [(100 \times 100) + (100 \times 1) + (5 \times 100) + (5 \times 1)] (100 + 2)$
$= (10000 + 100 + 500 + 5) (100 + 2) = (10605) (100 + 2)$

Now multiply the resulting expression:

$(10605) (100 + 2) = (10605 \times 100) + (10605 \times 2) = 1060500 + 21210 = 1081710$

Hence, $105 \times 101 \times 102 = 1081710$ .

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Similar questions

Find the number from each of the following expanded forms:

(a) 8 × 10⁴ + 6 × 10³ + 0 × 10² + 4 × 10¹ + 5 × 10⁰

(b) 4 × 10⁵+ 5 × 10³+ 3 × 10²+ 2 × 10⁰

(d) 9 × 10⁵ + 2 × 10² + 3 × 10¹

Write the numeral whose expanded form is given below:
(i) $6 \times 10^{4} + 3 \times 10^{3} + 0 \times 10^{2} + 7 \times 10^{1} + 8 \times 10^{0}$
(ii) $9 \times 10^{6} + 7 \times 10^{5} + 0 \times 10^{4} + 3 \times 10^{3} + 4 \times 10^{2} + 6 \times 10^{1} + 2 \times 10^{0}$
(iii) $8 \times 10^{5} + 6 \times 10^{4} + 4 \times 10^{3} + 2 \times 10^{2} + 9 \times 10^{1} + 6 \times 10^{0}$

Q. Question 2(d)
Find the number from each of the following expanded forms:
(d)

9 \times 10^{5} + 2 \times 10^{2} + 3 \times 10^{1}

(603 $\times$ 301) $\div$ (101 $\times$ 102) =?

Question 61

$876543 = 8 \times 10^{5} + 7 \times 10^{4} + 6 \times 10^{3} + 5 \times 10^{2} + 4 \times 10^{1} + 3 \times 10^{0}$

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Find the product of 105×101×102

Find the product of $105 \times 101 \times 102$