Question

❤♥️❤ QUESTION⤴️⤴️⤴️


PLSS HELP ME!!!! THERE R 2 QUESTIONS!!!


⭐⭐NOTE:-

⚪⚫ NO IRRELEVANT/WRONG ANSWERS!!! DON'T ANSWER IF U R NOT SURE!!✌✌

PLSSS MAADAT KARDO NA !!!:) :) ♥️​

Answer 1

Step-by-step explanation:

1) We have

12 = 2×2×3 = 2²×3¹

42 = 2¹×3¹×7¹

LCM(12,42)=2²×3¹×7¹ =84---(1)

/* Product of the greatest power of each prime factors of the numbers

But ,

LCM = 10m+4 [given]---(2)

(2)=(1)

10m+4 = 84

=> 10m+4 = 10×8+4

Compare both sides , we get

m = 8

2) $Expansion\: of \\\:\frac{441}{2^{2}\times 5^{3}\times 7} shows\: a \:terminating\: decimal.$

Explanation:

$Least\: form \:of \:given \:rational \:number \\\frac{441}{2^{2}\times 5^{3}\times 7}\\=\frac{7\times 63}{2^{2}\times 5^{3}\times 7}\\=\\\frac{63}{2^{2}\times 5^{3}}$

Now,

Denominator (q) = 2²×5³ is of the form $2^{n}\times 5^{m}$ , where n and m are non-negative integers .

Then given rational number has a decimal expansion which terminates.

Verification:

$\\\frac{441}{2^{2}\times 5^{3}\times 7}\\=\frac{7\times 63}{2^{2}\times 5^{3}\times 7}\\=\\\frac{63}{2^{2}\times 5^{3}}$

$\frac{2\times 63}{2^{3}\times 5^{3}}$

= $\frac{126}{(2\times 5)^{3}}$

=$\frac{126}{(10)^{3}}$

=$0.126$

/* Terminating decimal */

•••♪

Answer 2

Solution :-

1). If LCM if 12 and 42 is 10m + 4 then find the value of 'm'

By splitting 12 and 42 in its prime factors .

12 = 2² × 3

42 = 2 × 3 × 7

So we have the LCM

= 2² × 3 × 7

= 4 × 3 × 7

= 84

So as LCM is of the form

10m + 4

→ 84 = 10m + 4

By subtracting 4 from both the sides

→ 84 - 4 = 10m + 4 - 4

→ 80 = 10m

→m = 80 ÷ 10

→ m = 8

So Value of "m"

$\huge{\boxed{\sf{= 8}}}$

____________________________________

2. What type of decimal expansion of a number

$\dfrac{441}{2^2 \times 5^3 \times 7}$

Have ?

Let us reduce it step by step :-

$\dfrac{441}{2^2 \times 5^3 \times 7}$

$= \dfrac{7^2\times 3^2\times}{2^2 \times 5^3 \times 7}$

$= \dfrac{ 7 \times 3^2}{10^2 \times 5}$

$= \dfrac{63}{500}$

$= 0.126$

Hence it will have a

$\large{\boxed{\textsf{Teminating Decimal Expansion}}}$