It is given that p = 3.6 × 104 and q = 9 × 10⁻⁴. Find, giving the answers in standard form: a) pq b) p/q. 2)…

Question

It is given that p = 3.6 × 104 and q = 9 × 10⁻⁴. Find, giving the answers in standard form: a) pq b) p/q. 2) m = 2 × 103 and n = 5 × 10. Find: a) mn b) n/m.

ScanSolve AI Tutor · Accepted Answer

here are the solutions for the standard form problems.

1) Given $p = 3.6 \times 10^4$ and $q = 9 \times 10^4$ .

a) Find $pq$

Multiply the numerical parts and the powers of 10 separately.
$pq = (3.6 \times 10^4) \times (9 \times 10^4)$ $pq = (3.6 \times 9) \times (10^4 \times 10^4)$
Perform the multiplication and apply the exponent rule $a^m \times a^n = a^{m+n}$ .
$pq = 32.4 \times 10^{4+4}$ $pq = 32.4 \times 10^8$
Convert the result to standard form (a number between 1 and 10 multiplied by a power of 10).
$32.4 = 3.24 \times 10^1$ $pq = (3.24 \times 10^1) \times 10^8$ $pq = 3.24 \times 10^{1+8}$ $pq = \boxed{3.24 \times 10^9}$
b) Find $\frac{p}{q}$
Divide the numerical parts and the powers of 10 separately.
$\frac{p}{q} = \frac{3.6 \times 10^4}{9 \times 10^4}$ $\frac{p}{q} = \left(\frac{3.6}{9}\right) \times \left(\frac{10^4}{10^4}\right)$
Perform the division and apply the exponent rule $\frac{a^m}{a^n} = a^{m-n}$ .
$\frac{p}{q} = 0.4 \times 10^{4-4}$ $\frac{p}{q} = 0.4 \times 10^0$ $\frac{p}{q} = 0.4 \times 1$ $\frac{p}{q} = 0.4$
Convert the result to standard form.
$0.4 = 4 \times 10^{-1}$ $\frac{p}{q} = \boxed{4 \times 10^{-1}}$
2) Given $m = 2 \times 10^3$ and $n = 5 \times 10$ .
Note that $n = 5 \times 10^1$ .

a) Find $mn$
Multiply the numerical parts and the powers of 10 separately.
$mn = (2 \times 10^3) \times (5 \times 10^1)$ $mn = (2 \times 5) \times (10^3 \times 10^1)$
Perform the multiplication and apply the exponent rule $a^m \times a^n = a^{m+n}$ .
$mn = 10 \times 10^{3+1}$ $mn = 10 \times 10^4$
Convert the result to standard form.
$10 = 1 \times 10^1$ $mn = (1 \times 10^1) \times 10^4$ $mn = 1 \times 10^{1+4}$ $mn = \boxed{1 \times 10^5}$
b) Find $\frac{n}{m}$
Divide the numerical parts and the powers of 10 separately.
$\frac{n}{m} = \frac{5 \times 10^1}{2 \times 10^3}$ $\frac{n}{m} = \left(\frac{5}{2}\right) \times \left(\frac{10^1}{10^3}\right)$
Perform the division and apply the exponent rule $\frac{a^m}{a^n} = a^{m-n}$ .
$\frac{n}{m} = 2.5 \times 10^{1-3}$ $\frac{n}{m} = 2.5 \times 10^{-2}$
This result is already in standard form.
$\frac{n}{m} = \boxed{2.5 \times 10^{-2}}$

It is given that p = 3.6 x 104 and q = 9 x 10⁻⁴. Find, giving the answers in standard form: a) pq b) p/q. 2) m = 2 x 103 and n = 5 x 10. Find: a) mn b) n/m.

Step-by-step solution

Multiply the numerical parts and the powers of 10 separately.

Perform the multiplication and apply the exponent rule $a^m \times a^n = a^{m+n}$ .

Convert the result to standard form (a number between 1 and 10 multiplied by a power of 10).

Divide the numerical parts and the powers of 10 separately.

Perform the division and apply the exponent rule $\frac{a^m}{a^n} = a^{m-n}$ .

Convert the result to standard form.

Multiply the numerical parts and the powers of 10 separately.

Perform the multiplication and apply the exponent rule $a^m \times a^n = a^{m+n}$ .

Convert the result to standard form.

Divide the numerical parts and the powers of 10 separately.

Perform the division and apply the exponent rule $\frac{a^m}{a^n} = a^{m-n}$ .

Still stuck on this one?

More Mathematics Questions

It is given that p = 3.6 x 104 and q = 9 x 10⁻⁴. Find, giving the answers in standard form: a) pq b) p/q. 2) m = 2 x 103 and n = 5 x 10. Find: a) mn b) n/m.

Step-by-step solution

Multiply the numerical parts and the powers of 10 separately.

Perform the multiplication and apply the exponent rule am×an=am+na^m \times a^n = a^{m+n}am×an=am+n.

Convert the result to standard form (a number between 1 and 10 multiplied by a power of 10).

Divide the numerical parts and the powers of 10 separately.

Perform the division and apply the exponent rule aman=am−n\frac{a^m}{a^n} = a^{m-n}anam​=am−n.

Convert the result to standard form.

Multiply the numerical parts and the powers of 10 separately.

Perform the multiplication and apply the exponent rule am×an=am+na^m \times a^n = a^{m+n}am×an=am+n.

Convert the result to standard form.

Divide the numerical parts and the powers of 10 separately.

Perform the division and apply the exponent rule aman=am−n\frac{a^m}{a^n} = a^{m-n}anam​=am−n.

Still stuck on this one?

More Mathematics Questions

Perform the multiplication and apply the exponent rule $a^m \times a^n = a^{m+n}$ .

Perform the division and apply the exponent rule $\frac{a^m}{a^n} = a^{m-n}$ .

Perform the multiplication and apply the exponent rule $a^m \times a^n = a^{m+n}$ .

Perform the division and apply the exponent rule $\frac{a^m}{a^n} = a^{m-n}$ .