Question 5

In the following figure, screws are placed above a scale. Measure them and write their length in the space provided.

Which scale helped you measure the length of the screws accurately? Why?

What is the meaning of $2 \dfrac{7}{10} \text{ cm}$ (the length of the first screw)?

Context: As seen on the ruler, the unit length between two consecutive numbers is divided into 10 equal parts. To get the length $2\dfrac{7}{10}\text{ cm}$, we go from 0 to 2 and then take seven parts of $\dfrac{1}{10}$. The length of the screw is $2\text{ cm}$ and $\dfrac{7}{10}\text{ cm}$. Similarly, we can make sense of the length $3\dfrac{2}{10}\text{ cm}$.

Q. Can you explain why the unit was divided into smaller parts to measure the screws?

Write the measurements of the objects shown in the picture:

For the objects shown below, write their lengths in two ways and read them aloud. An example is given for the USB cable. (Note that the unit length used in each diagram is not the same).

Arrange these lengths in increasing order:

(a) $\dfrac{9}{10}$

(b) $1 \dfrac{7}{10}$

(c) $\dfrac{130}{10}$

(d) $13 \dfrac{1}{10}$

(e) $10 \dfrac{5}{10}$

(f) $7 \dfrac{6}{10}$

(g) $6 \dfrac{7}{10}$

(h) $\dfrac{4}{10}$

Arrange the following lengths in increasing order: $4\dfrac{1}{10}$, $\dfrac{4}{10}$, $\dfrac{41}{10}$, $41\dfrac{1}{10}$.

The lengths of the body parts of a honeybee are given. Find its total length.

Head: $2\dfrac{3}{10}$ units Thorax: $5\dfrac{4}{10}$ units Abdomen: $7\dfrac{5}{10}$ units

The length of Shylaja's hand is $12\dfrac{4}{10}$ units, and her palm is $6\dfrac{7}{10}$ units, as shown in the picture. What is the length of the longest (middle) finger?

Context: The length of Shylaja's hand is $12 \dfrac{4}{10}$ units, and her palm is $6 \dfrac{7}{10}$ units.

Q. Try computing the difference by converting both lengths to tenths.

A Celestial Pearl Danio's length is $2\dfrac{4}{10} \text{ cm}$, and the length of a Philippine Goby is $\dfrac{9}{10} \text{ cm}$. What is the difference in their lengths?

How big are these fish compared to your finger?

Observe the given sequences of numbers. Identify the change after each term and extend the pattern:

(a) $4$, $4\dfrac{3}{10}$, $4\dfrac{6}{10}$, ______, ______, ______

(b) $8\dfrac{2}{10}$, $8\dfrac{7}{10}$, $9\dfrac{2}{10}$, ______, ______, ______

(c) $7\dfrac{6}{10}$, $8\dfrac{7}{10}$, ______, ______, ______, ______

(d) $5\dfrac{7}{10}$, $5\dfrac{3}{10}$, ______, ______, ______, ______

(e) $13\dfrac{5}{10}$, $13$, $12\dfrac{5}{10}$, ______, ______, ______, ______

(f) $11\dfrac{5}{10}$, $10\dfrac{4}{10}$, $9\dfrac{3}{10}$, ______, ______, ______

What is the length of this smaller part? How many such smaller parts make a unit length?

How many one-hundredths make one-tenth? Can we also say that the length is 4 units and 45 one-hundredths?

Observe the figure below. Notice the markings and the corresponding lengths written in the boxes when measured from $0$. Fill the lengths in the empty boxes.

For the lengths shown below write the measurements and read out the measures in words.

In each group, identify the longest and the shortest lengths. Mark each length on the scale.

(a) $\dfrac{3}{10}, \dfrac{3}{100}, \dfrac{33}{100}$

(b) $3\dfrac{1}{10}, \dfrac{30}{10}, 1\dfrac{3}{10}$

(c) $\dfrac{45}{100}, \dfrac{54}{100}, \dfrac{5}{10}, \dfrac{4}{10}$

(d) $3\dfrac{6}{10}, 3\dfrac{6}{100}, 3\dfrac{6}{10}\dfrac{6}{100}$

(e) $\dfrac{8}{10}, \dfrac{2}{100}, \dfrac{9}{100}, 1\dfrac{8}{100}$

(f) $7\dfrac{3}{10}\dfrac{5}{100}, 7\dfrac{5}{10}, 7\dfrac{41}{100}$

(g) $\dfrac{65}{10}\dfrac{15}{100}, 5\dfrac{87}{100}, 5\dfrac{7}{100}$

Context: What will be the sum of $15\ \dfrac{3}{10}\ \dfrac{4}{100}$ and $2\ \dfrac{6}{10}\ \dfrac{8}{100}$? This can be solved in different ways. Some are shown below.

Are both these methods different?

Observe the addition done below for $483 + 268$. Do you see any similarities between the methods shown above?

Can we extend this further?

We can ask similar questions about fractional parts:

(a) How many thousandths make one unit? (b) How many thousandths make one tenth? (c) How many thousandths make one hundredth? (d) How many tenths make one ten? (e) How many hundredths make one ten?

Make a few more questions of this kind and answer them.

Can the quantity $4 \dfrac{2}{10}$ be written as 42 (skipping the $\dfrac{1}{10}$ in $2 \times \dfrac{1}{10}$)?

If yes, how would we know if 42 means 4 tens and 2 units or it means 4 units and 2 tenths?

Make a place value table similar to the one above. Write each quantity in decimal form and in terms of place value, and read the number:

(a) 2 ones, 3 tenths and 5 hundredths

(b) 1 ten and 5 tenths

(c) 4 ones and 6 hundredths

(d) 1 hundred, 1 one and 1 hundredth

(e) $\dfrac{8}{100}$ and $\dfrac{9}{10}$

(f) $\dfrac{5}{100}$

(g) $\dfrac{1}{10}$

(h) $2\dfrac{1}{100}$, $4\dfrac{1}{10}$ and $7\dfrac{7}{1000}$

Write these quantities in decimal form:

(a) 234 hundredths

(b) 105 tenths

Fill in the blanks below ($\text{mm} \leftrightarrow \text{cm}$)

Fill in the blanks below ($\text{cm} \leftrightarrow \text{m}$):

How many mm does 1 meter have?

Can we write $1\text{ mm} = \dfrac{1}{1000}\text{ m}$?

Fill in the blanks below ($\text{g} \rightleftarrows \text{kg}$)

Fill in the blanks below (rupee $\leftrightarrow$ paise)

Name all the divisions between $1$ and $1.1$ on the number line.

Identify and write the decimal numbers against the letters.