Question

9 × 10^5 is(A) ______times as larger as 3 ×10^3 5× 10^-3 is( B)______time as smaller as 5 × 10^-2

Answer 1

A) To know how many times greater 9*10⁵ is from 3*10³, you have to divide both values:

$\frac{9\cdot10^5}{3\cdot10^3}$

You can divide this fraction into two:

$\frac{9}{3}\cdot\frac{10^5}{10^3}$

And solve them separatelly, afterwards you can multiply the results of both fractions:

$\frac{9}{3}=3$$\frac{10^5}{10^3}=10^{5-3}=10^2$

Note: when you divide two exponents values with the same base number, you have to subtract both exponent numbers.

Multiply both results:

$3\cdot10^2=300$

9*10⁵ is A. 300 times larger as 3*10³

B) To calculate how many times 5*10⁻³ is smaller than 5*10⁻², you have to divide the greater number by the smaller number.

$\frac{5\cdot10^{-2}}{5\cdot10^{-3}}$

Following the same procedure as before:

$\frac{5}{5}\cdot\frac{10^{-2}}{10^{-3}}$$\frac{5}{5}=1$

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

Reunite both values:

$1\cdot10^1=10$

5*10⁻³ is B. 10 times smaller as 5*10⁻²