Tag: number names, numerals and place values

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Questions Related to number names, numerals and place values

Multiple choice maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

Which of the following statement is false?

  1. $\displaystyle 4\cdot 59\times 10^{-3}=0.00459$
  2. $\displaystyle 7\times 10^{-5}=0.00007$
  3. $\displaystyle 1\cdot 03\times 10^{-3}=1030$
  4. $\displaystyle 8\cdot 8\times 10^{-4}=0.00088$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\displaystyle 1\cdot 03\times 10^{-3}= 0\cdot 00103$
$\displaystyle \therefore $ The given statement is false

Multiple choice maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

Which of the following expressions is true?

  1. $2940000=$$\displaystyle 2\cdot 94\times 10^{5}$
  2. $502000=$$\displaystyle 5\cdot 02\times 10^{5}$
  3. $3683000=$$\displaystyle 3\cdot 683\times 10^{5}$
  4. $40404000=$$\displaystyle 4\cdot 0404\times 10^{5}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\displaystyle 502000= 5\cdot 02\times 10^{5}$

Therefore, option B is correct.

Multiple choice maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

When $70, 000$ is written as $7.0\times10^n$, what is the value of $n$?

  1. $1$
  2. $2$
  3. $3$
  4. $4$
  5. $5$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given that $70,000$ is written as $7.0$ $\times $ ${10}^{n}$

From this, we can write
$70,000$ $=$ $7.0$ $\times$ ${10}^{n}$
$\Rightarrow {10}^{n}$ $=$ $\dfrac {70,000}{7}$
$\Rightarrow {10}^{n}$ $=$ $10,000$
$\Rightarrow {10}^{n}$ $=$ ${10}^{4}$
$\Rightarrow n$ $=$ $\log _{10}$ ${10}^{4}$
$\Rightarrow n$ $=$ $4$ $\log _{10}$ $10$
$\Rightarrow $ $=$ $4$
Therefore, the value of $n$ is $'4'$.

Multiple choice maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

The value of $\dfrac{(10^4+324)(22^4+324)(34^4+324)(46^4+324)(58^4+324)}{(4^4+324)(16^4+324)(28^4+324)(40^4+324)(52^4+324)}$ is?

  1. $324$
  2. $400$
  3. $373$
  4. $1024$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This expression uses the Sophie Germain identity: a^4 + 4b^4 = (a^2 + 2b^2 + 2ab)(a^2 + 2b^2 - 2ab). Here, 324 = 4 * 81 = 4 * 3^4, so b=3. Applying this to each term allows for cancellation of factors between the numerator and denominator, leaving only the ratio of the remaining terms.

Multiple choice maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

Find the last two digits of $3^{1997}$.

  1. $67$
  2. $63$
  3. $80$
  4. $56$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is same as asking what is remainder when $3^{1997}\div 100$
$3^{4}\equiv 81  mod  100$
$3^{8}\equiv 61  mod  100$
$3^{12}\equiv 41  mod  100$
$3^{16}\equiv 21  mod  100$
$3^{20}\equiv 1  mod  100$


Now, $3^{40}, 3^{60}, 3^{80}, 3^{100}, ...., 3^{1980}$ all are $\equiv 1  mod  100$

We know $3^{16}\equiv 21  mod  100$

$3^{17}\equiv 21\times 3  mod  100$

$3^{17}\equiv 63  mod  100$

$\therefore 3^{1997}\equiv 3^{1980}\times 3^{17}$

since, $3^{1980}\equiv 1  mod  100$

and $3^{17}\equiv 63  mod  100$

$\therefore 3^{1997}\equiv 63  mod  100$

$\therefore $ Last two digit is 63