Chapter 7, Problem 1NT

In a set of base-ten blocks, let 1 flat represents 1 unit.

a. What does 1 long represents?

b. What does 1 cube represents?

c. Represent 1.23 using the blocks with these representations.

To determine

(a)

To find:

In a set of base-ten block, 1 long represents.

Answer to Problem 1NT

Solution:

1 long represents $\frac{1}{10}$.

Explanation of Solution

Given:

In a set of base-ten blocks, 1 flat represents 1 unit.

Approach:

Write decimal in form of tenths and hundredths.

Calculation:

There are 10 block/ long in 1 flat.

$\begin{array}{c}10\text{ long =}1\text{ flat}\\ \text{1 long = }\frac{1}{10}\text{ flat }\mathrm{......}\text{(1)}\\ \text{=0}\text{.1 flat}\end{array}$

Hence, 1 long/ block represents 0.1 flat.

To determine

(b)

To find:

In a set of base-ten block, 1 cube represents.

Answer to Problem 1NT

Solution:

1 cube represents $\frac{1}{100}\text{ or }\mathrm{0.01.}$

Explanation of Solution

Given:

In a set of base-ten blocks, 1 flat represents 1 unit.

Approach:

Write decimal in form of tenths and hundredths.

Calculation:

There are again 10 cubes in 1 long.

$\begin{array}{l}10\text{ cube =}1\text{ long}\\ \text{1 cube}=\frac{1}{10}\text{ long}\end{array}$

By equation (1)

$\begin{array}{rll}\text{1 cube}& =& \frac{1}{10}\times \frac{1}{10}\text{ flat}\\ & =& \frac{1}{100}\\ & =& 0.01\text{ flat}\text{.}\end{array}$

Hence, 1 cube represents 0.01 flat.

To determine

(c)

To represent:

The number 1.23 using blocks.

Answer to Problem 1NT

Solution:

The representation of 1.23 is

Explanation of Solution

Given:

In a set of base-ten blocks, 1 flat represents 1 unit.

Approach:

Write decimal in form of tenths and hundredths.

Calculation:

Here

1 long = 0.1 flat

1 cube = 0.01 flat

$\begin{array}{rll}1.23& =& 1+0.2+0.03\\ & =& 1+\frac{2}{10}+\frac{3}{100}\end{array}$

Here 1 represent 1 flat,

$\frac{2}{10}$ represents 2 longs.

$\frac{3}{100}$ represents 3 cubes.