Can the quantity be written as 42 (skipping the in )? If yes, how would we know if 42 means 4 tens and 2 units or it means 4 units and 2 tenths?

The way we write numbers tells us the value of each digit. Step 1 — Understanding We first convert the mixed number to a decimal. A mixed number has a whole part and a fractional part. The number means 4 whole units plus two tenths. We can write two tenths as a decimal. > This number has 4 in the units place. It has 2 in the tenths place. Step 2 — Understanding the number 42 Now, let us look at the number 42. This number is a whole number. Each digit in a whole number has a place value. The digit on the right is in the units place. The digit to its left is in the tens place. > This number has 4 in the tens place. It has 2 in the units place. Step 3 — Comparing the two numbers We found the value of . We also found the value of 42. The value of is 4.2. The value of 42 is 42. These two numbers are not the same. So, cannot be written as 42. Step 4 — How we distinguish values The decimal point is very important in numbers. It separates the whole number part from the fractional part. If a number has no decimal point, it is a whole number. For example, 42 means 4 tens and 2 units. To show 4 units and 2 tenths, we use a decimal point. We write it as 4.2. The position of each digit tells us its value. This system is called place value. Answer > (i) No, the quantity cannot be written as 42. > (ii) We know the difference by looking at the decimal point and the place value of each digit. > (iii) The number 42 means 4 tens and 2 units, while 4.2 means 4 units and 2 tenths.

A Peek Beyond the Point | IT

Question 28

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

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

Solution

The way we write numbers tells us the value of each digit.

Step 1 — Understanding $4 \frac{2}{10}$

We first convert the mixed number to a decimal. A mixed number has a whole part and a fractional part. The number $4 \frac{2}{10}$ means 4 whole units plus two tenths. We can write two tenths as a decimal.

$4 \frac{2}{10} = 4 + \frac{2}{10}$

$= 4 + 0.2$

$\boxed{4.2}$

This number has 4 in the units place. It has 2 in the tenths place.

Step 2 — Understanding the number 42

Now, let us look at the number 42. This number is a whole number. Each digit in a whole number has a place value. The digit on the right is in the units place. The digit to its left is in the tens place.

$42 = 4 \times 10 + 2 \times 1$

$= 40 + 2$

$\boxed{42}$

This number has 4 in the tens place. It has 2 in the units place.

Step 3 — Comparing the two numbers

We found the value of $4 \frac{2}{10}$ . We also found the value of 42. The value of $4 \frac{2}{10}$ is 4.2. The value of 42 is 42. These two numbers are not the same. So, $4 \frac{2}{10}$ cannot be written as 42.

Step 4 — How we distinguish values

The decimal point is very important in numbers. It separates the whole number part from the fractional part. If a number has no decimal point, it is a whole number. For example, 42 means 4 tens and 2 units. To show 4 units and 2 tenths, we use a decimal point. We write it as 4.2. The position of each digit tells us its value. This system is called place value.

Answer

(i) No, the quantity $4 \frac{2}{10}$ cannot be written as 42. (ii) We know the difference by looking at the decimal point and the place value of each digit. (iii) The number 42 means 4 tens and 2 units, while 4.2 means 4 units and 2 tenths.

More questions in IT

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 $2 \frac{7}{10}$ 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 $2\frac{7}{10}\text{ cm}$ , we go from 0 to 2 and then take seven parts of $\frac{1}{10}$ . The length of the screw is $2\text{ cm}$ and $\frac{7}{10}\text{ cm}$ . Similarly, we can make sense of the length $3\frac{2}{10}\text{ cm}$ .

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

Measure the following objects using a scale and write their measurements in centimeters (as shown earlier for the lengths of the screws): pen, sharpener, and any other object of your choice.

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) $\frac{9}{10}$

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

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

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

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

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

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

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

Q10

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

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

Q11

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

Q12

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

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

Q13

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

Q14

How big are these fish compared to your finger?

Q15

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

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

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

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

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

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

Q16

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

Q17

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

Q18

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.

Q19

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

Q20

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

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

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

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

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

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

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

Q21

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

Are both these methods different?

Q22

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

$(400 + 80 + 3) + (200 + 60 + 8)$

$= (400 + 200) + (80 + 60) + (3 + 8)$

$= 600 + 140 + 11$

$= 600 + 150 + 1$

$= 700 + 50 + 1$

$= 751$

Q25

Can we extend this further?

Q26

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?

Q27

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

Q28

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