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Use of exponents - class-VII

Description: use of exponents
Number of Questions: 41
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Tags: repeated multiplication square and square root real numbers exponents and powers numbers indices powers and exponents fractions and standard forms basic algebra maths fundamentals
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Evaluate the product of $2.3\times 10^4$ and $3\times 10^3$.

maths square and square root scientific notation use of exponents power of 10

  1. $6.9\times 10^4$

  2. $6.9\times 10^7$

  3. $6.9\times 10^8$

  4. $6.9\times 10^6$

Show answer
Correct Option: B
Explanation:

$(2.3\times 10^4) \times (3 \times 10^3)$
$\Rightarrow (2.3 \times 3) \times(10^{3+4})$

$\therefore 6.9 \times 10^7$
Ans- Option $B$.

Evaluate $\dfrac{6.3\times 10^3}{3\times 10^7}$

maths square and square root scientific notation use of exponents power of 10

  1. $2\times 10^{-3}$

  2. $2.1\times 10^{-3}$

  3. $2.1\times 10^{-4}$

  4. $2\times 10^{-5}$

Show answer
Correct Option: C
Explanation:

$\dfrac{6.3\times 10^{3}}{3\times 10^7}$


$\Rightarrow \dfrac{6.3}{3} \times 10^{3-7}$


$\therefore 2.1\times 10^{-4}$

Ans-Option $C$.

Solve:

$\cfrac{2.3^{n+1} + 7.3^{n-1}}{3^{n+2}-2 \left ( \cfrac{1}{3} \right )^{1-n}} $

maths square and square root scientific notation use of exponents power of 10

  1. $0$

  2. $1$

  3. $2$

  4. $3$

Show answer
Correct Option: B
Explanation:

We have,

$\cfrac{2.3^{n+1} + 7.3^{n-1}}{3^{n+2}-2 \left ( \cfrac{1}{3} \right )^{1-n}}  $

$\Rightarrow \cfrac{6.3^n+ \dfrac{7}{3}.3^n}{9.3^n-\dfrac{2}{3}. 3^n}  $

$\Rightarrow \cfrac{18.3^n+ 7.3^n}{27.3^n-2. 3^n}  $

$\Rightarrow \cfrac{25.3^n}{25.3^n}  $

$\Rightarrow 1  $

Hence, this is the answer.

The average distance between the Sun and a certain planet is approximately $\displaystyle 2.3\times { 10 }^{ 14 }$ inches. Which of the following is closest to the average distance between the Sun and the planet, in kilometers? (1 kilometer is approximately $\displaystyle 3.9\times { 10 }^{ 4 }$ inches )

maths square and square root scientific notation use of exponents power of 10

  1. $\displaystyle 7.1\times { 10 }^{ 8 }$

  2. $\displaystyle 5.9\times { 10 }^{ 9 }$

  3. $\displaystyle 1.6\times { 10 }^{ 10 }$

  4. $\displaystyle 1.6\times { 10 }^{ 111 }$

  5. $\displaystyle 5.9\times { 10 }^{ 11 }$

Show answer
Correct Option: B
Explanation:

The average distance in KM will be $\frac { 2.3\times { 10 }^{ 14 } }{ 3.9\times { 10 }^{ 4 } } =0.59\times { 10 }^{ 10 }=5.9\times { 10 }^{ 9 }\quad km$

So correct answer will be option B

Simplify: $\dfrac{1.8\times 10^{11}}{2\times 10^4}$

maths square and square root scientific notation use of exponents power of 10

  1. $9\times 10^7$

  2. $0.9\times 10^6$

  3. $0.9\times 10^5$

  4. $9\times 10^6$

Show answer
Correct Option: D
Explanation:

$\dfrac{1.8\times 10^{11}}{2\times 10^4}$


$= \dfrac{1.8}{2} \times 10^{11-4}$


$=0.9 \times 10^7$

$= 9\times 10^6$


Ans-Option $D$.

Express $(3000)^2\times (20)^3$ in scientific notation:

maths square and square root scientific notation use of exponents power of 10

  1. $7.2\times 10^{10}$

  2. $3.6\times 10^{8}$

  3. $6\times 10^9$

  4. $4.8\times 10^{12}$

Show answer
Correct Option: A
Explanation:

${ 3000 }^{ 2 }\times { 20 }^{ 3 }=(9\times { 10 }^{ 6 })\times (8\times { 10 }^{ 3 })\ =72\times { 10 }^{ 9 }=7.2\times { 10 }^{ 10 }$

So correct answer will be option A

Standard form of $900000000 + 800000 + 50000 + 3000 + 20 + 3$ is

maths square and square root scientific notation use of exponents power of 10

  1. $90,00,85,323$

  2. $9,85,03,023$

  3. $90,08,53,023$

  4. $9,85,323$

Show answer
Correct Option: C
Explanation:

Standard form of $900000000 + 800000 + 50000 + 3000 + 20 + 3 = 90,08,53,023$
$\therefore$ Option C is correct.

Which of the following number is in the scientific notation?

maths square and square root scientific notation use of exponents power of 10

  1. $\displaystyle 1.26\times 10^{-5}$ m

  2. $\displaystyle 15.75\times 10^{3}$ km

  3. $\displaystyle 0.18\times 10^{-7}$ km

  4. $\displaystyle 0.0013\times 10^{-8}$ km

Show answer
Correct Option: A
Explanation:

Since $\displaystyle 1 \leq 1.26<10$  

The number shuold be in between 1 and 10

Standard form of 
$900000000+3000+7$ is

maths square and square root scientific notation use of exponents power of 10

  1. $90003007$

  2. $900003007$

  3. $900003000$

  4. none

Show answer
Correct Option: B
Explanation:

Standard form of $900000000 + 3000+7=900003007$

The population of India is close to $1.08 \times  10^{9}$. Which of the following represents this population written in standard notation?

maths square and square root scientific notation use of exponents power of 10

  1. 1,080,000,000

  2. 1,080,000

  3. 180,000,000

  4. 108,000

Show answer
Correct Option: A
Explanation:

We get the answer by multiplying and dividing the number by ${ 10 }^{ 9}=1000000000$

The airports in the United States serve more than 635,000,000 people each year. Which of the following is the same number written in scientific notation?

maths square and square root scientific notation use of exponents power of 10

  1. $635 \times 10^6$

  2. $6.35 \times 10^8$

  3. $6.35 \times 10^{-8}$

  4. $6.35 \times 10^9$

Show answer
Correct Option: B
Explanation:

We get the answer by multiplying and dividing the number by 100000000 = ${ 10 }^{ 8 }$

Numeral for sixty million and sixty six is

maths square and square root scientific notation use of exponents power of 10

  1. 60,000,060

  2. 60,000,066

  3. 6,000,066

  4. none of these

Show answer
Correct Option: B
Explanation:

Numeral for sixty million and sixty six is 60,000,066.

Commas are inserted in a number after each

maths square and square root scientific notation use of exponents power of 10

  1. place

  2. digit

  3. period

  4. none of these

Show answer
Correct Option: C
Explanation:

Commas are inserted in a number after each period.
Example 39,54, 452

9849475825 is written with commas as (International System)

maths square and square root scientific notation use of exponents power of 10

  1. 9,84,94,75,825

  2. 9,849,475,825

  3. 9849,475,82,5

  4. 9,8,4,9,4,7,5,8,2,5

Show answer
Correct Option: B
Explanation:

International System: 9,849,475,825

Places in ones period are

maths square and square root scientific notation use of exponents power of 10

  1. ones and tens

  2. ones, tens and hundreds

  3. tens and hundreds

  4. ones, hundreds and thousands

Show answer
Correct Option: B
Explanation:

In Indian and international system in the both cases ones period has 3 places
= ones, tens, hundreds

$10$ crore= ....... million

maths square and square root scientific notation use of exponents power of 10

  1. 10

  2. 100

  3. 1

  4. 1000

Show answer
Correct Option: B
Explanation:

10 crores (or 1000 lakhs) is equal to 100 million (0.1 billion)

How many symbols are used in Roman numerals ?

maths square and square root scientific notation use of exponents power of 10

  1. 7

  2. 6

  3. 9

  4. 12

Show answer
Correct Option: A
Explanation:

There are seven basic symbols,

$I, V, X, L, C, D$ and $M$.

 

Hence, this is the answer. 

Which of the following are NOT correctly matched?

maths square and square root scientific notation use of exponents power of 10

  1. I = 7

  2. X = 10

  3. V = 2

  4. XII = 12

Show answer
Correct Option: A,C
Explanation:

We know that

$I=1, V=5, X=10,XII = 12$

So, $V$ can not equal to $2$ and $I$ can not equal to $7$

Hence, this is the answer.

A number which is a factor of every number is

maths square and square root scientific notation use of exponents power of 10

  1. 0

  2. 1

  3. 2

  4. none of these

Show answer
Correct Option: B
Explanation:

1 is the factor of every number .

Which option has same value as $10+10^3$

maths square and square root scientific notation use of exponents power of 10

  1. $2.0\times 10^3$

  2. $8.0\times 10^3$

  3. $4.0\times 10^1$

  4. $1.01\times 10^3$

Show answer
Correct Option: D
Explanation:

$10+{ 10 }^{ 3 }=10+1000=1010=1.01\times { 10 }^{ 3 }$

So correct answer will be option D

Write $1000000+200000+70000$ in scientific notation.

maths square and square root scientific notation use of exponents power of 10

  1. $1.27\times 10^5$

  2. $1.27\times 10^6$

  3. $3.7\times 10^6$

  4. $1.9\times 10^5$

Show answer
Correct Option: B
Explanation:

$1000000+200000+70000=1270000$

$\therefore 12700000=1.27\times 10^6$
Ans-Option $B$.

Write $4.5\times 10^5$ in decimal form

maths square and square root scientific notation use of exponents power of 10

  1. $450000$

  2. $45000$

  3. $4500$

  4. $4500000$

Show answer
Correct Option: A
Explanation:

$4.5\times 10^5=450000$

Ans-Option $A$.

Express $0.008712$ in scientific notation.

maths square and square root scientific notation use of exponents power of 10

  1. $8.712\times 10^3$

  2. $8.712\times 10^{-3}$

  3. $8.712\times 10^{-4}$

  4. $8.712\times 10^{-2}$

Show answer
Correct Option: B
Explanation:

$0.008712=8.712\times 10^{-3}$

Ans-Option $B$

Write $50000+4000+20+9$ in standard form.

maths square and square root scientific notation use of exponents power of 10

  1. $54290$

  2. $5429$

  3. $54209$

  4. $54029$

Show answer
Correct Option: D
Explanation:

We need to write it in a standard form:

$50000+4000+20+9$
$=54000+20+9$
$=54020+9$
$=54029$
Ans-Option $D$.

Write $8.73\times 10^7$ in standard form.

maths square and square root scientific notation use of exponents power of 10

  1. $8730000$

  2. $873000$

  3. $87300000$

  4. $83700000$

Show answer
Correct Option: C
Explanation:

$8.73\times 10^7=87300000$

Ans-Option $C$

Write the following in scientific notation: $(200)^3$

maths square and square root scientific notation use of exponents power of 10

  1. $4\times 10^4$

  2. $8\times 10^6$

  3. $6\times 10^6$

  4. $8\times 10^8$

Show answer
Correct Option: B
Explanation:

$(200)^3=2^3\times 10^6$

$\Rightarrow (200)^3=8\times 10^6$
Ans-Option $B$.

Write in scientific notation: $(400000)^4$

maths square and square root scientific notation use of exponents power of 10

  1. $6.4\times 10^{20}$

  2. $2.56\times 10^{20}$

  3. $2.56\times 10^{22}$

  4. $6.4\times 10^{19}$

Show answer
Correct Option: C
Explanation:

$(400000)^4=4^4\times 10^{20}$

$\Rightarrow (400000)^4=256\times 10^{20}=2.56\times 10^{22}$
Ans-Option $C$.

The scientific notation of $923.4$ is

maths square and square root scientific notation use of exponents power of 10

  1. $9.234\times { 10 }^{ -2 }$

  2. $9.234\times { 10 }^{ 2 }$

  3. $9.234\times { 10 }^{ 3 }$

  4. $9.234\times { 10 }^{ -3 }$

Show answer
Correct Option: B
Explanation:

$923.4 = 9.234 \times 100$


In scientific notation, $923.4 = 9.234 \times 10^{2}$

The scientific notation of $0.00036$ is

maths square and square root scientific notation use of exponents power of 10

  1. $3.6\times { 10 }^{ -3 }$

  2. $3.6\times { 10 }^{ 3 }$

  3. $3.6\times { 10 }^{ -4 }$

  4. $3.6\times { 10 }^{ 4 }$

Show answer
Correct Option: C
Explanation:

$0.00036 = \dfrac{36}{10000} = 36\times10^{-5}$


$\therefore$ Scientific notation $= 3.6 \times 10^{-4}$

The decimal form of $2.57\times { 10 }^{ 3 }$ is

maths square and square root scientific notation use of exponents power of 10

  1. $257$

  2. $2570$

  3. $25700$

  4. $257000$

Show answer
Correct Option: B
Explanation:

$2.57 \times 10^{3} = 2.57 \times 1000 = 2570$

$\therefore$ answer is $2570$.

The decimal form of $3.506\times { 10 }^{ -2 }$ is

maths square and square root scientific notation use of exponents power of 10

  1. $0.03506$

  2. $0.003506$

  3. $35.06$

  4. $350.6$

Show answer
Correct Option: A
Explanation:

$3.506 \times 10^{-2} = \dfrac{3.506}{100} = 0.03506$


$\therefore$ answer is $0.03506$

State the following statement is True or False
$9.954\times 10^4$ can be written as $9954$

maths square and square root scientific notation use of exponents power of 10

  1. True

  2. False

Show answer
Correct Option: B
Explanation:
$9.954\times 10^4$ can be written as 
$9.954\times 10000=99540$
Thus statement is false as $9.954\times 10^4$ is not equal to $9954$.

In scientific notation, the numbers to the left and right to the decimal point are known as __________ and ________ respectively.

maths square and square root scientific notation use of exponents power of 10

  1. Coefficient, Mantissa

  2. Mantissa, Coefficient

  3. Standard form, Scientific form

  4. Scientific form, Standard form

Show answer
Correct Option: A
Explanation:

Take example $7.495$

In scientific notation the number present left to decimal point is called $coefficient$ and the number present right to decimal point is $Mantissa$ 

The digit in the ten's place of a two-digit number is three times that in the one's places if the digits are reversed the new number will be 36 less than the original number Find the number 

maths square and square root scientific notation use of exponents power of 10

  1. 64

  2. 52

  3. 62

  4. 42

Show answer
Correct Option: C
Explanation:

Let the digits be $ x $ and $ y $
Given, "The digit in the ten's place of a two-digit number is three times that in the one's places "
$ => x = 3y $ 

Now, when the digits are reversed, the number will be $ 10y + x $
Also,  if the digits are reversed the new number will be $ 36 $ less than the original number. $ => 10y + x = (10x + y) - 36 $
$ => 9x -9y = 36 $

Putting $ x = 3y $ in this,
$ 9(3y) -9y = 36 $
$ => 27y - 9y = 36 $
$ 18y = 36 => y = 2 $

So, $ x = 3y = 6 $
Hence, the number is $ 62 $

Express $2.53\times 10^{-4}$ in standard notation

maths square and square root scientific notation use of exponents power of 10

  1. $2.53$

  2. $0.0000253$

  3. $0.00253$

  4. $0.000253$

Show answer
Correct Option: D
Explanation:

$2.53\times { 10 }^{ -4 }=\frac { 2.53 }{ { 10 }^{ 4 } } =0.000253$

So correct answer will be option D

Convert $62000+39000$ to scietific form.

maths square and square root scientific notation use of exponents power of 10

  1. $1.01\times 10^5$

  2. $1.1\times 10^5$

  3. $1.01\times 10^4$

  4. $1.1\times 10^4$

Show answer
Correct Option: A
Explanation:

On adding, we get

$62000+39000=101000$
Therefore, $ 101000=1.01\times 10^5$
Hence, option A is correct.

Convert $6.634\times 10^{-3}$ in decimal form.

maths square and square root scientific notation use of exponents power of 10

  1. $6634$

  2. $0.006634$

  3. $0.006643$

  4. $0.0006634$

Show answer
Correct Option: B
Explanation:

$6.634\times 10^{-3}$ can be written as 

$=\dfrac{6.634}{1000}=0.006634$
Hence, option B is correct.

Write $1200\times 3200$ in scientific notation.

maths square and square root scientific notation use of exponents power of 10

  1. $384000$

  2. $384\times 10^3$

  3. $3.84\times 10^6$

  4. $3840\times10^2$

Show answer
Correct Option: C
Explanation:

The value of $3200\times 1200$ is 

$=32\times12\times10^4\=384\times 10^4\=3.84\times 10^6$

Which of the following options is INCORRECT?

maths square and square root scientific notation use of exponents power of 10

  1. The number $48693$ rounded off to nearest hundred is $48700$

  2. LXXV is greater than LXXIV

  3. One million is equal to $10$ crore

  4. Place value of a digit $=$(face value of the digit)$\times$ (Value of the place)

Show answer
Correct Option: C
Explanation:

Option A: For rounding to the nearest hundred, If tens digit is 0,1,2,3,4

, then round down to the previous hundred and If tens digit is 5,6,7,8,9, then round up to the next hundred.
Following the above rule, as 6 is present in the hundredth place, we will round up it to $700$.

Hence $48693$ $\rightarrow$ $48700$.

Option B: LXXV $\rightarrow$ $75$
                 LXXIV $\rightarrow$ $74$
So, LXXV $>$ LXXIV

Option C: 1 million $\rightarrow$ 10,00,000 $\rightarrow$ 10lakh

Option D: Face value is the value of the digit itself.
Value of place if the position of the digit in the number
Hence, Place value $\rightarrow$ face value $\times$ Value of place

Hence Option C is incorrect.





In scientific notation, $670,000,000 + 700,000,000 =$?

maths square and square root scientific notation use of exponents power of 10

  1. $1.37 \times {10}^{-9}$

  2. $1.37 \times {10}^{7}$

  3. $1.37 \times {10}^{8}$

  4. $1.37 \times {10}^{9}$

  5. $137 \times {10}^{15}$

Show answer
Correct Option: D
Explanation:

$670,000,000+700,000,000=1,370,000,000$

$\therefore 1,370,000,000=1.37\times 10^9$
Ans-Option $D$.

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