Place Value and the Number System: Practice

Reading from the right, the places are ones, tens, hundreds, thousands, ten-thousands. The $6$ sits in the ten-thousands place.

$6 \times 10{,}000 = 60{,}000$

The $5$ is worth $50{,}000$, the $4$ is in the hundreds place, and the $9$ is worth $9$; the two zeros contribute nothing.

$50{,}409 = 50{,}000 + 400 + 9$

Both have five digits and tie through the thousands place, so compare the hundreds: $9$ against $8$.

$9 > 8 \;\Rightarrow\; 34{,}900 > 34{,}890$

All tie at $4$ thousands, so compare the hundreds: $4{,}120$ has $1$ (least), and the other two have $2$. Between those, compare the tens: $4{,}201$ has $0$, $4{,}210$ has $1$.

$4{,}120 < 4{,}201 < 4{,}210$

Write one three-digit block for each period. The thousands period is $305$, and the ones period is $060$ because sixty has to fill all three of its columns.

$305{,}060$

Drop that padding zero and the blocks join up as $30{,}560$, in which the $3$ is worth $30{,}000$ instead of $300{,}000$.

Read the columns from the right: $3$ ones, $1$ ten, $5$ hundreds, $7$ thousands, $2$ ten-thousands.

$7 \times 1{,}000 = 7{,}000$

So the $7$ sits in the thousands place.

The $9$ is worth $9{,}000$, the $6$ is in the hundreds place, the tens digit is $0$, and the $3$ is worth $3$.

$9{,}603 = 9{,}000 + 600 + 3$

Group into periods: $812$ (thousands), $067$ (ones). Inside $812$, the $8$ is the hundreds slot of the thousands period, the hundred-thousands place.

$8 \times 100{,}000 = 800{,}000$

Group into periods: $403$ (thousands) and $060$ (ones). Read each group, then its period name.

$403{,}060 = (403 \times 1{,}000) + 60$

So it reads "four hundred three thousand, sixty."

All tie at $27$ thousands, so compare the hundreds: $27{,}005$ and $27{,}050$ have $0$, the others have $5$. Between those two, compare the tens: $0$ against $5$.

$27{,}005 < 27{,}050$

So $27{,}005$ is smallest.

Group into periods: $1$ (millions), $480$ (thousands), $300$ (ones). Inside $480$, the $4$ is the hundreds slot of the thousands period.

$4 \times 100{,}000 = 400{,}000$

That is the hundred-thousands place.

All three tie in the thousands place, so compare the hundreds: $1$, $0$, $0$. That puts $8{,}190$ first. The remaining two tie in the hundreds as well, so compare their tens: $9$ against $1$.

$8{,}190 > 8{,}091 > 8{,}019$