Question

10×22×(0.01×10-²)² / 7×50×10‐⁵​

Answer 1

ㅤㅤㅤ☆Given to simplify:-

$\tt \: l = \dfrac{10 \times 22 \times (0.01 \times 10 {}^{ - 2}) {}^{2} }{7 \times 50 \times 10 {}^{ - 8} }$

☆EXPLANATION

$\tt \: l = \dfrac{1 \not0 \times 22 \times (0.01 \times 10 {}^{ - 2}) {}^{2} }{7 \times 5 \not0 \times 10 {}^{ - 8} }$

$\tt \: l = \dfrac{1 \times 22 \times (0.01) {}^{2} \times (10 {}^{ - 2}) {}^{2} }{7 \times 5 \times 10 {}^{ - 8} }$

$\tt \: l = \dfrac{ 22 \times (0.01 \times 0.01) \times (10 {}^{ - 4}) }{35 \times 10 {}^{ - 8} }$

➳ 0.01 can be written as 10 ⁻²

➳10⁻² × 10⁻² can be simplified byadding the powers .

$\tt \: l = \dfrac{ 22 \times (10 {}^{ - 2} \times 10 {}^{ - 2} ) \times (10 {}^{ - 4}) }{35 \times 10 {}^{ - 8} }$

$\tt \: l = \dfrac{ 22 \times 10 {}^{ - 4} \times 10 {}^{ - 4} }{35 \times 10 {}^{ - 8} }$

➳10⁻⁴ × 10⁻⁴ can be simplified by adding the powers.

$\tt \: l = \dfrac{ 22 \times 10 {}^{ - 4 - 4} }{35 \times 10 {}^{ - 8} }$

$\tt \: l = \dfrac{ 22 \times 10 {}^{ - 8 } }{35 \times 10 {}^{ - 8} }$

➳Cancelling 10⁻⁸ to the numerator and denominator .

$\tt \: l = \dfrac{ 22 }{35 }$

➳Writing in decimal forms .

$\tt \: l = 0.628$