Expanding a Rational Number Using Powers

Q.

How to express $2$ power $16$ ?

Q. Question 1(v)
Write the following numbers in the expanded form:
(v) 20, 068

Q.

What value of x makes "5 raised to the power x" equal to 25 ?

1. 2

2. 5

3. -2

4. -5

Q. Question 1(iii)
Write the following numbers in the expanded form:
(iii) 28, 06, 196

Q.

$3\times 1000+2\times 10+\frac{4}{10}+\frac{3}{1000}$is the expanded form of the number ____.

1. $3200.430$

2. $3002.403$

3. $32.430$

4. $3020.403$

Q.

Question 61

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

Q.

The scientific notation of 165000000000000 is given by:

1. $1.65\times {10}^{13}$

2. $16.5\times {10}^{12}$

3. $1650\times {10}^{12}$

4. $1.65\times {10}^{14}$

Q.

Find the number from each of the following expanded forms: ${3\times 10}^4+{7\times 10}^2+{5\times 10}^0$.

Q. Evaluate :

xi) $6.3÷(0.3{)}^2$

Q.

Question 63

$4\times {10}^5+3\times {10}^4+2\times {10}^3+1\times {10}^0=432010$

Q. Question 2(c)
Find the number from each of the following expanded forms:
(c) $3\times {10}^4+7\times {10}^2+5\times {10}^0$

Q.

State whether the given statement is True or False: One million $={10}^7$

1. True
2. False

Q.

4329 = ___

1. $(9\times {10}^0)+(2\times {10}^1)+(3\times {10}^2)+(4\times {10}^3)$

2. $(4\times {10}^{-3})+(3\times {10}^1)+(2\times {10}^2)+(9\times {10}^3)$

3. $(4\times {10}^{-3})+(3\times {10}^{-2})+(2\times {10}^{-1})+(9\times {10}^0)$

4. $(9\times {10}^{-3})+(2\times {10}^{-2})+(3\times {10}^{-1})+(4\times {10}^3)$

Q. The numerical value of
$5\times {10}^2+3\times {10}^1+6\times {10}^0+0\times {10}^{-1}+7\times {10}^{-2}$ is _____.

1. 536.07
2. 563.7
3. 536.7
4. 563.07

Q. Simplify:

Q. Expanded form of 51280 is $5\times {10}^4+1\times {10}^a+2\times {10}^2+8\times {10}^b+0$.
Find the value of a and b.

1. a=1, b=3
2. a=3, b=1
3. a=3, b=2
4. a=4, b=2

Q. Simplify: $(2^{20}÷2^{15})\times 2^3$

1. $2^8$
2. $2^{15}$
3. $2^4$
4. $2^2$

Q. Simpify and express following as a rational number :
${\left(\frac{3}{4}\right)}^2\times {\left(\frac{-1}{2}\right)}^5\times 2^3$

Q.

Write the following in the expanded notation

$49.137$

Q. 3 $\times$ ${10}^2$ + 2 $\times$ ${10}^1$ + 9 $\times$ ${10}^0$ + 2 $\times$ ${10}^{-1}$ + 5 $\times$ ${10}^{-2}$ can be expressed as

1. 32.925
2. 3292.5
3. 329.25
4. 3.2925

Q.

Find the number from the expanded form:

1 ×${10}^5$ + 0 × ${10}^4$ + 4 ×${10}^3$ + 2 ×${10}^2$ + 7 ×${10}^1$ + 8 ×${10}^0$

Q.

Question 64

$8\times {10}^6+2\times {10}^4+5\times {10}^2+9\times {10}^0=8020509$

Q. Express the following as a product of prime factors only in exponential form:
$108\times 192$

[3 marks]
[NCERT-Ex 13.2, Q4(i)]
[Exponential form of numbers]

Q.

$4^2\times 3^2=4\times$ ___ $\times 3\times 3$ Fill in the blank [Enter a numerical value].

___

Q. Find the value of $(2\times {10}^4)+(5\times {10}^3)+(4\times {10}^2)+(3\times {10}^1)+(6\times {10}^0)+(7\times {10}^{-1})+(8\times {10}^{-2})+(9\times {10}^{-3})$

1. 2543.789
2. 2543.6789
3. 2543.6789
4. 25436.789

Q.

ADDING AND SUBTRACTING IN SCIENTIFIC NOTATION

Find the sum or difference. Write your answer in scientific notation.

$(9.2\times {10}^8)–(4\times {10}^8)$

Q. $7\times {10}^3+4\times 10+1\times {10}^{-1}+8\times {10}^{-3}$ is the expanded form of the number ____.

1. $7040.108$
2. $7040.018$
3. $7040.180$
4. $70400.108$

Q. Find the numerical value of $x$ from the diagram given below:

Q. 555 can be expressed as

1. $5\times {10}^2+5\times {10}^1+5\times {10}^0$
2. $5\times {10}^1+5\times {10}^0+5\times {10}^{-1}$
3. $5\times {10}^{-2}+5\times {10}^0+5\times {10}^1$

Q.

If 3676.48 can be written in expanded form as:
$3\times {10}^a+b\times {10}^2+7\times {10}^c+6\times {10}^0+4\times {10}^d+e\times {10}^{-2}$ .
$\text{Find the value of}a+b-c-d-e.$

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