The number 0-00000000016 when expressed in standard form is written as 1 - a - 10 b- Find the value of a -1 b-A- 70B- 61C- 60D- -70

The correct option is D 700.00000000016=16/10^11 =1.6× 10/10^11 nbsp; =1.6× 10^ 10 (Using a^m/a^n=a^m n) Since 1.a × 10^b=1.6× 10^ 10, we have a = 6 and b = ...

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Standard IX

Mathematics

Scientific Representation of Decimal Number

The number 0....

Question

The number $0.00000000016$ when expressed in standard form is written as $1. a \times 10^{b} .$ Find the value of $(a + 1) b$ .

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-70

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Solution

The correct option is D -70
$0.00000000016 = \frac{16}{10^{11}}$
$= \frac{1.6 \times 10}{10^{11}}$
$= 1.6 \times 10^{- 10}$
(Using $\frac{a^{m}}{a^{n}} = a^{m - n}$ )
Since $1. a \times 10^{b} = 1.6 \times 10^{- 10},$ we have
$a = 6$ and $b = - 10.$
$∴ (a + 1) b = (6 + 1) (- 10) = - 70$

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The number 0.00000000016 when expressed in standard form is written as 1.a×10b. Find the value of (a+1)b.

The correct option is D -700.00000000016=161011 =1.6×101011 =1.6×10−10 (Using aman=am−n) Since 1.a×10b=1.6×10−10, we have a=6 and b=−10. ∴(a+1)b=(6+1)(−10)=−70

The number $0.00000000016$ when expressed in standard form is written as $1. a \times 10^{b} .$ Find the value of $(a + 1) b$ .

The correct option is D -70
$0.00000000016 = \frac{16}{10^{11}}$
$= \frac{1.6 \times 10}{10^{11}}$
$= 1.6 \times 10^{- 10}$
(Using $\frac{a^{m}}{a^{n}} = a^{m - n}$ )
Since $1. a \times 10^{b} = 1.6 \times 10^{- 10},$ we have
$a = 6$ and $b = - 10.$
$∴ (a + 1) b = (6 + 1) (- 10) = - 70$