Chapter 3, Problem 1NT

NOW TRY THIS

a. Trade base-ten blocks (as shown in Figure 2) to write $3$ blocks, $12$ flats, $11$ longs and $17$ units with the fewest number of blocks. What Hindu-Arabic numeral is represented by these blocks?

b. Write $3282$ in expanded form.

To determine

a.

To find:

The Hindu-Arabic numeral represented by the given blocks.

Answer to Problem 1NT

Solution:

The Hindu-Arabic numeral represented by the given blocks is $4327$.

Explanation of Solution

Given:

The given base-ten blocks are $3$ blocks, $12$ flats, $11$ longs and $17$ units.

Approach:

A block consists of units, longs, flats and blocks representing $1s$, $10s$, $100s$ and $1000s$ respectively.

Calculation:

The trading the given blocks for as fewest blocks possible is shown below.

$\begin{array}{rll}\text{3}\text{blocks 12 flats}\text{11 longs 17 units }& =& \text{ 3 blocks; 1 block}\text{2 flats; 10 longs}\text{1 long; 10 units}\text{7 units}\\ & =& \text{ 4 blocks}\text{2 flats; 1 flat}\text{1 long; 1 long}\text{7 units}\\ & =& \text{ 4 blocks}\text{3 flats}\text{2 longs}\text{7 units}\\ & =& \text{ 4327}\end{array}$

Hence, the Hindu-Arabic numeral represented by the given blocks is $4327$.

To determine

b.

To find:

The expanded form of given numeral $3282$.

Answer to Problem 1NT

Solution:

The expanded form of $3282$ is $3\times {10}^3+2\times {10}^2+8\times 10+2\times 1$.

Explanation of Solution

Given:

The given numeral is $3282$.

Approach:

The place value from right to left is written as ones, tens, hundreds and so on.

Calculation:

The expanded form of given numeral is

$\begin{array}{rll}3282& =& 3\times 1000+2\times 100+8\times 10+2\times 1\\ & =& 3\times {10}^3+2\times {10}^2+8\times 10+2\times 1\end{array}$.

Hence, the expanded form of $3282$ is $3\times {10}^3+2\times {10}^2+8\times 10+2\times 1$.