Tag: numbers in general form

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Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

Expanded form of 78.059 is

  1. $78\, +\, \displaystyle \frac {5}{10}\, +\, \displaystyle \frac {9}{100}$
  2. $70\, +\,8\, +\,0\, +\, \displaystyle \frac {5}{100}\, +\, \displaystyle \frac {9}{1000}$
  3. $70\, +\,8\, +\, \displaystyle \frac {5}{10}\, +\, \displaystyle \frac {9}{100}$

  4. None
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  The given number is $78.059$

$\Rightarrow$  Expanded form = $70+8+0+\dfrac{5}{100}+\dfrac{9}{1000}$

Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

If $(2t - 3)(? + 6 + 9) = 8t$$^3$ $- 27$, then ? will be replaced by 

  1. $-4t$$^2$
  2. $5t$$^2$
  3. $4t$$^2$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$8t^3$ $- 27 = (2t)$$^3$ $- (3)$$^3$
$= (2t - 3)$$[(2t)$$^2$ $+ 2t \times 3 + 3$$^2$]
$= (2t - 3)(4t$^2$ + 6t + 9)$
$\because$ $(2t - 3)(4t$$^2$ $+ 6t + 9)$
$= (2t - 3)(a + 6t + 9)$
$\Rightarrow$ $4t$$^2$ $+ 6t + 9 = (a + 6t + 9)$
$\therefore$ $a = 4t$$^2$