Place Value and the Number System: Additional Practice (Set 2)

The $8$ sits in the ten-thousands place, whose place value is $10{,}000$, and the $5$ sits in the tens place, whose place value is $10$. Divide the two place values.

$\frac{10{,}000}{10} = 1{,}000$

So the $8$'s place value is $1{,}000$ times the $5$'s.

"How many hundreds" asks how many groups of $100$ fit inside the number, not which digit sits in the hundreds column.

$73{,}500 = 735 \times 100$

So $73{,}500$ is $735$ hundreds.

In $1{,}632$ the $6$ is in the hundreds place, worth $600$. Ten times that value is $6{,}000$, which is the thousands place.

$10 \times 600 = 6{,}000$

Only $16{,}320$ has its $6$ in the thousands place (worth $6{,}000$). In $632$ the $6$ is worth $600$, in $3{,}061$ it is worth $60$, and in $60{,}300$ it is worth $60{,}000$.

A value of $9{,}000$ puts the $9$ in the thousands place.

$9 \times 1{,}000 = 9{,}000$

In $59{,}000$ the $9$ is in the thousands place. In the others the $9$ is worth $90$, $900$, or $90{,}000$.

Read the places of $80{,}040$ from the right: $0$ ones, $4$ tens, $0$ hundreds, $0$ thousands, $8$ ten-thousands. The $8$ is in the ten-thousands place, not the thousands place.

$8 \times 10{,}000 = 80{,}000$

The $4$ is in the tens place, and the number reads "eighty thousand forty," so the other statements are false.

The $8$ is in the thousands place (value $8{,}000$) and the $4$ is in the hundreds place (value $400$). Divide the two values.

$\frac{8{,}000}{400} = 20$

The first $7$ is in the hundreds place (value $700$) and the second is in the ones place (value $7$). Divide the values.

$\frac{700}{7} = 100$

So the first $7$ is worth $100$ times the second.

The tens digit is $7$. Increasing only that digit by $2$ makes it $9$; every other place stays the same.

$7 + 2 = 9 \;\Rightarrow\; 8{,}473 \to 8{,}493$

Write one three-digit block for each period: $904$ thousands and $030$ ones. Thirty is padded to $030$ so that the ones period fills all three of its columns.

$904{,}030$

Drop that padding zero and the blocks join up as $90{,}430$, in which the $9$ is worth $90{,}000$ instead of $900{,}000$.

Between $700$ and $800$ forces a $7$ in the hundreds place, and the ones digit is $5$, so the number looks like $7\square 5$. The digit sum is $15$, so the tens digit is $15 - 7 - 5 = 3$.

$7 + 3 + 5 = 15 \;\Rightarrow\; 735$

The leftmost $4$ is in the thousands place (value $4{,}000$) and the rightmost $4$ is in the ones place (value $4$). Subtract to find how much one exceeds the other.

$4{,}000 - 4 = 3{,}996$

To maximize the number, put the largest digit in the highest place and continue in decreasing order: $9$, then $5$, then $2$, then $0$.

$9 \mid 5 \mid 2 \mid 0 = 9{,}520$