Place Value and the Number System: Additional Practice (Set 1)

Label the places of $7{,}248{,}091$ from the right: ones $1$, tens $9$, hundreds $0$, thousands $8$, ten-thousands $4$, hundred-thousands $2$, millions $7$.

$2 \times 100{,}000 = 200{,}000$

So the digit in the hundred-thousands place is $2$.

The $4$ is in the hundreds place (value $400$) and the $8$ is in the ones place (value $8$). Divide the two values.

$\frac{400}{8} = 50$

So the $4$ is worth $50$ times the $8$.

Place each digit in its named column: ten-thousands $6$, thousands $0$, hundreds $3$, tens $0$, ones $7$.

$(6 \times 10{,}000) + (3 \times 100) + (7 \times 1) = 60{,}307$

In $2{,}734$ the $7$ is in the hundreds place, worth $700$. Ten times that value is $7{,}000$, the thousands place.

$10 \times 700 = 7{,}000$

Only $17{,}340$ has its $7$ in the thousands place.

Add the place values, keeping a $0$ in any place that has no term (the thousands place here).

$40{,}000 + 600 + 50 + 2 = 40{,}652$

"How many tens" asks how many groups of $10$ make up the whole number, not which digit sits in the tens column.

$9{,}060 = 906 \times 10$

So $9{,}060$ is $906$ tens.

All four are built from the same digits, so the columns they sit in decide the order. The four tie in the ten-thousands and in the thousands, so compare the hundreds: $6$, $6$, $0$, $8$.

$52{,}806 > 52{,}680 > 52{,}608 > 52{,}086$

The largest hundreds digit settles it before the tens are read at all.

A four-digit number cannot start with $0$, so put the smallest nonzero digit, $1$, in the thousands place, then fill the rest in increasing order with $0, 3, 8$.

$1 \mid 0 \mid 3 \mid 8 = 1{,}038$

Split the digits into periods from the right: $6$ millions, $050$ thousands, $300$ ones. Say each block followed by its period name.

$6{,}050{,}300$

The thousands block is $050$, which is fifty, not five and not thirty.

Read the places of $50{,}604$ from the right: ones $4$, tens $0$, hundreds $6$, thousands $0$, ten-thousands $5$.

$5 \times 10{,}000 = 50{,}000$

The $6$ is in the hundreds place, the $4$ is in the ones place, and the number reads "fifty thousand six hundred four," so only the statement about the $5$ is true.

The leftmost $2$ is in the thousands place (value $2{,}000$) and the other $2$ is in the tens place (value $20$). Subtract to find how much one exceeds the other.

$2{,}000 - 20 = 1{,}980$

Compare each candidate with the two bounds, place by place from the left.

$5{,}200 < 5{,}260 < 5{,}300$

The others fall outside: $5{,}198$ and $5{,}030$ are below $5{,}200$, and $5{,}320$ is above $5{,}300$.