If

then we should have

Differentiating with respect to
gives


So
is indeed conservative, and

Expanded Numbers Form:
<span><span> 4,000,000 </span><span>+500,000 </span><span>+0 </span><span>+8,000 </span><span>+200 </span><span>+20 </span><span>+7 </span></span>
Expanded Factors Form:
<span><span> 4 ×1,000,000 </span><span>+5 ×100,000 </span><span>+0 ×10,000 </span><span>+8 ×1,000 </span><span>+2 ×100 </span><span>+2 ×10 </span><span>+7 ×1 </span></span>
Expanded Exponential Form:
<span><span>4 × 106</span><span>+<span>5 × 105</span></span><span>+<span>0 × 104</span></span><span>+<span>8 × 103</span></span><span>+<span>2 × 102</span></span><span>+<span>2 × 101</span></span><span>+<span>7 × 100</span></span></span>
Word Form:
four million,
five hundred eight thousand,
<span>two hundred twenty-seven</span>