Write the number $1010.0101$ using base $10$ and exponents.

(1010.0101)_{10} = 10^{2} + 10^{1} + \frac{1}{10^{2}} + \frac{1}{10^{4}}

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(1010.0101)_{10} = 10^{3} + 10^{1} + \frac{1}{10^{2}} + \frac{1}{10^{4}}

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(1010.0101)_{10} = 10^{3} + 10^{1} + \frac{1}{10^{2}} + \frac{1}{10^{3}}

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(1010.0101)_{10} = 10^{4} + 10^{1} + \frac{1}{10^{2}} + \frac{1}{10^{4}}

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Solution

The correct option is B $(1010.0101)_{10} = 10^{3} + 10^{1} + \frac{1}{10^{2}} + \frac{1}{10^{4}}$
The given number is $1010.0101$
It can be written as
$1 \times 10^{3} + 0 \times 10^{2} + 1 \times 10^{1} + 0 \times 10^{0} + 0 \times 10^{- 1} + 1 \times 10^{- 2} + 0 \times 10^{- 3} + 1 \times 10^{- 4}$
$= 10^{3} + 10^{1} + \frac{1}{10^{2}} + \frac{1}{10^{4}}$
Hence, $(1010.0101)_{10} = 10^{3} + 10^{1} + \frac{1}{10^{2}} + \frac{1}{10^{4}}$

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Similar questions

Write the numeral whose expanded form is given below:
(i) $6 \times 10^{4} + 3 \times 10^{3} + 0 \times 10^{2} + 7 \times 10^{1} + 8 \times 10^{0}$
(ii) $9 \times 10^{6} + 7 \times 10^{5} + 0 \times 10^{4} + 3 \times 10^{3} + 4 \times 10^{2} + 6 \times 10^{1} + 2 \times 10^{0}$
(iii) $8 \times 10^{5} + 6 \times 10^{4} + 4 \times 10^{3} + 2 \times 10^{2} + 9 \times 10^{1} + 6 \times 10^{0}$

Find the number from each of the following expanded forms:

(a) 8 × 10⁴ + 6 × 10³ + 0 × 10² + 4 × 10¹ + 5 × 10⁰

(b) 4 × 10⁵+ 5 × 10³+ 3 × 10²+ 2 × 10⁰

(d) 9 × 10⁵ + 2 × 10² + 3 × 10¹

$(\frac{1}{10}) + {(\frac{1}{10})}^{2} + {(\frac{1}{10})}^{3} + {(\frac{1}{10})}^{4} =$ ?

Find the value of

$(2 \times 10^{4}) + (3 \times 10^{3}) + (1 \times 10^{2}) + (6 \times 10^{1}) + (7 \times 10^{0}) + (4 \times 10^{- 1}) + (2 \times 10^{- 2}) + (8 \times 10^{- 3})$

Q. Express the number :

8 \times 10^{5} + 7 \times 10^{4} + 5 \times 10^{3} + 4 \times 10^{2} + 6 \times 10^{1} + 9 \times 10^{0}

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Write the number 1010.0101 using base 10 and exponents.

The correct option is B (1010.0101)10=103+101+1102+1104The given number is 1010.0101It can be written as 1×103+0×102+1×101+0×100+0×10−1+1×10−2+0×10−3+1×10−4=103+101+1102+1104Hence, (1010.0101)10=103+101+1102+1104

Write the number $1010.0101$ using base $10$ and exponents.