Question

1) work out the value of (1.7x10^4)x (8.5x10^-2) give your answer in standard form.

Answer 1

ANSWER TO QUESTION 1

$(1.7\times 10^4)\times(8.5\times 10^{-2})$

We rewrite to obtain;

$(1.7\times 10^4)\times(8.5\times 10^{-2})=(1.7\times 8.5)\times(10^4\times 10^{-2})$

Recall this product law of indices

$a^m\times a^n=a^{m+n}$

we apply this law to obtain,

$(1.7\times 10^4)\times(8.5\times 10^{-2})=14.45\times10^{4+-2}$

This simplifies to

$(1.7\times 10^4)\times(8.5\times 10^{-2})=14.45\times10^{2}$

We need to rewrite this in standard form;

$(1.7\times 10^4)\times(8.5\times 10^{-2})=1.445\times 10^1\times10^{2}$

We apply the product law again to get

$(1.7\times 10^4)\times(8.5\times 10^{-2})=1.445\times 10^{1+2}$

This simplifies to

$(1.7\times 10^4)\times(8.5\times 10^{-2})=1.445\times 10^{3}$

ANSWER TO QUESTION 2

$(6.8\times 10^2)\times(1.3\times 10^{-3})$

We rewrite to obtain;

$(6.8\times 10^2)\times(1.3\times 10^-3)=(6.8\times 1.3)\times(10^2\times 10^{-3})$

Recall this product law of indices

$a^m\times a^n=a^{m+n}$

we apply this law to obtain,

$(6.8\times 10^2)\times(1.3\times 10^-3)=8.84\times10^{2+-3}$

This simplifies to

$(6.8\times 10^2)\times(1.3\times 10^-3)=8.84\times10^{-1}$

This is already in standard form.