# Decimals - Class 6 - Mathematics

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## Examples - Decimals | NCERT | Mathematics | Class 6

Which is greater? with steps

(a) 1 or 0.99

(b) 1.09 or 1.093

To determine which number is greater in each pair, we can compare them directly.

### (a) 1 vs 0.99

Compare the whole number parts: Both numbers have a whole number part of 1 and 0 respectively.

Since 1 is greater than 0.99 based on their whole number part,

**1 is greater than 0.99**.

### (b) 1.09 vs 1.093

Compare the whole number parts: Both numbers have a whole number part of 1.

Compare the tenths: Both numbers have the same tenths digit (0).

Compare the hundredths: Both numbers have the same hundredths digit (9).

Compare the thousandths: 1.09 has an implied zero in the thousandths place, while 1.093 has a 3 in the thousandths place.

Since 3 is greater than 0 in the thousandths place,

**1.093 is greater than 1.09**.

Lata spent ₹ 9.50 for buying a pen and ₹ 2.50 for one pencil. How much money did she spend?

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Sign up nowSamson travelled $5 \mathrm{~km} 52 \mathrm{~m}$ by bus, $2 \mathrm{~km} 265 \mathrm{~m}$ by car and the rest $1 \mathrm{~km} 30 \mathrm{~m}$ he walked. How much distance did he travel in all?

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Sign up nowRahul bought $4 \mathrm{~kg} 90 \mathrm{~g}$ of apples, $2 \mathrm{~kg} 60 \mathrm{~g}$ of grapes and $5 \mathrm{~kg} 300 \mathrm{~g}$ of mangoes. Find the total weight of all the fruits he bought.

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Sign up nowAbhishek had ₹ 7.45. He bought toffees for ₹ 5.30. Find the balance amount left with Abhishek.

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Urmila's school is at a distance of $5 \mathrm{~km} 350 \mathrm{~m}$ from her house. She travels $1 \mathrm{~km} 70 \mathrm{~m}$ on foot and the rest by bus. How much distance does she travel by bus?

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Kanchan bought a watermelon weighing $5 \mathrm{~kg} 200 \mathrm{~g}$. Out of this she gave $2 \mathrm{~kg} 750 \mathrm{~g}$ to her neighbour. What is the weight of the watermelon left with Kanchan?

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## Exercise 8.1 - Decimals | NCERT | Mathematics | Class 6

Which is greater? with steps

(a) 0.3 or 0.4

(b) 0.07 or 0.02

(c) 3 or 0.8

(d) 0.5 or 0.05

(e) 1.23 or 1.2

(f) 0.099 or 0.19

(g) 1.5 or 1.50

(h) 1.431 or 1.490

(i) 3.3 or 3.300

(j) 5.64 or 5.603

Make five more examples and find the greater number from them.

To determine which number is greater in each pair, we'll compare them based on their decimal values.

**(a) 0.3 or 0.4**: 0.4 is greater than 0.3 because when comparing decimals, a larger number in the tenths place indicates a larger overall value.

**(b) 0.07 or 0.02**: 0.07 is greater than 0.02 because it has a larger number in the hundredths place.

**(c) 3 or 0.8**: 3 is greater than 0.8 because an integer value is generally greater than a decimal less than 1.

**(d) 0.5 or 0.05**: 0.5 is greater than 0.05 because a larger number in the tenths place (compared to the hundredths place in the smaller number) indicates it is larger.

**(e) 1.23 or 1.2**: 1.23 is greater than 1.2 because the additional hundredths place in 1.23 indicates a greater value.

**(f) 0.099 or 0.19**: 0.19 is greater than 0.099 because the tenths place is larger in 0.19.

**(g) 1.5 or 1.50**: These numbers are equal. However, conventionally 1.5 is considered the same value as 1.50.

**(h) 1.431 or 1.490**: 1.490 is greater than 1.431 because the hundredths place is higher.

**(i) 3.3 or 3.300**: These numbers are equal. Decimal places following a numeral don’t affect the value unless they add significant digits beyond zero.

**(j) 5.64 or 5.603**: 5.64 is greater than 5.603 because the hundredths place is larger.

**For the additional examples, let's create and compare:**

**(k) 0.89 or 0.9**: 0.9 is greater because the tenths place is higher.

**(l) 2.33 or 2.3**: 2.33 is greater because the hundredths place adds more value.

**(m) 0.111 or 0.12**: 0.12 is greater because the tenths place is higher, impacting the overall value more significantly.

**(n) 1.007 or 1.07**: 1.07 is greater because the hundredths place contributes more to its value than the thousandths place in 1.007.

**(o) 4.444 or 4.45**: 4.45 is greater because the tenths and hundredths places combined give it a higher value than 4.444, despite the thousandths place.

In summary:

- (a) 0.4
- (b) 0.07
- (c) 3
- (d) 0.5
- (e) 1.23
- (f) 0.19
- (g) Equal
- (h) 1.490
- (i) Equal
- (j) 5.64
- (k) 0.9
- (l) 2.33
- (m) 0.12
- (n) 1.07
- (o) 4.45

## Exercise 8.2 - Decimals | NCERT | Mathematics | Class 6

Express as rupees using decimals.

(a) 5 paise

(b) 75 paise

(c) 20 paise

(d) 50 rupees 90 paise

(e) 725 paise

To express the given values in rupees using decimals, we need to remember that 1 rupee = 100 paise. Therefore, to convert paise to rupees, we divide the amount of paise by 100. Let's perform these conversions for each case:

(a) 5 paise in rupees: $$ \frac{5 , \text{paise}}{100} = 0.05 , \text{rupees} $$

(b) 75 paise in rupees: $$ \frac{75 , \text{paise}}{100} = 0.75 , \text{rupees} $$

(c) 20 paise in rupees: $$ \frac{20 , \text{paise}}{100} = 0.20 , \text{rupees} $$

(d) For 50 rupees 90 paise, we express 90 paise in rupees and add it to the 50 rupees: $$ 90 , \text{paise} = \frac{90}{100} = 0.90 , \text{rupees} $$ Therefore, $$ 50 , \text{rupees} + 0.90 , \text{rupees} = 50.90 , \text{rupees} $$

(e) 725 paise in rupees: $$ \frac{725 , \text{paise}}{100} = 7.25 , \text{rupees} $$

Summary:

- (a) 0.05 rupees
- (b) 0.75 rupees
- (c) 0.20 rupees
- (d) 50.90 rupees
- (e) 7.25 rupees

Express as metres using decimals.

(a) $15 \mathrm{~cm}$

(b) $6 \mathrm{~cm}$

(c) $2 \mathrm{~m} 45 \mathrm{~cm}$

(d) $9 \mathrm{~m} 7 \mathrm{~cm}$

(e) $419 \mathrm{~cm}$

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Express as cm using decimals.

(a) $5 \mathrm{~mm}$

(b) $60 \mathrm{~mm}$

(c) $164 \mathrm{~mm}$

(d) $9 \mathrm{~cm} 8 \mathrm{~mm}$

(e) $93 \mathrm{~mm}$

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Express as km using decimals.

(a) $8 \mathrm{~m}$

(b) $88 \mathrm{~m}$

(c) $8888 \mathrm{~m}$

(d) $70 \mathrm{~km} 5 \mathrm{~m}$

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Express as kg using decimals.

(a) $2 \mathrm{~g}$

(b) $100 \mathrm{~g}$

(c) $3750 \mathrm{~g}$

(d) $5 \mathrm{~kg} 8 \mathrm{~g}$

(e) $26 \mathrm{~kg} 50 \mathrm{~g}$

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## Exercise 8.3 - Decimals | NCERT | Mathematics | Class 6

Find the sum in each of the following : with steps

(a) $0.007+8.5+30.08$

(b) $15+0.632+13.8$

(c) $27.076+0.55+0.004$

(d) $25.65+9.005+3.7$

(e) $0.75+10.425+2$

(f) $280.69+25.2+38$

The sums of each of the given expressions are as follows:

(a) $0.007 + 8.5 + 30.08 = 38.587$

(b) $15 + 0.632 + 13.8 = 29.432$

(c) $27.076 + 0.55 + 0.004 = 27.63$

(d) $25.65 + 9.005 + 3.7 = 38.355$

(e) $0.75 + 10.425 + 2 = 13.175$

(f) $280.69 + 25.2 + 38 = 343.89$

Rashid spent ₹ 35.75 for Maths book and ₹ 32.60 for Science book. Find the total amount spent by Rashid.

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Radhika's mother gave her $₹ 10.50$ and her father gave her $₹ 15.80$, find the total amount given to Radhika by the parents.

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Nasreen bought $3 \mathrm{~m} 20 \mathrm{~cm}$ cloth for her shirt and $2 \mathrm{~m} 5 \mathrm{~cm}$ cloth for her trouser. Find the total length of cloth bought by her.

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Naresh walked $2 \mathrm{~km} 35 \mathrm{~m}$ in the morning and $1 \mathrm{~km} 7 \mathrm{~m}$ in the evening. How much distance did he walk in all?

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Sunita travelled $15 \mathrm{~km} 268 \mathrm{~m}$ by bus, $7 \mathrm{~km} 7 \mathrm{~m}$ by car and $500 \mathrm{~m}$ on foot in order to reach her school. How far is her school from her residence?

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Ravi purchased $5 \mathrm{~kg} 400 \mathrm{~g}$ rice, $2 \mathrm{~kg} 20 \mathrm{~g}$ sugar and $10 \mathrm{~kg} 850 \mathrm{~g}$ flour. Find the total weight of his purchases.

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## Exercise 8.4 - Decimals | NCERT | Mathematics | Class 6

Subtract:

(a) ₹ 18.25 from ₹ 20.75

(b) $202.54 \mathrm{~m}$ from $250 \mathrm{~m}$

(c) ₹ 5.36 from ₹ 8.40

(d) $2.051 \mathrm{~km}$ from $5.206 \mathrm{~km}$

(e) $0.314 \mathrm{~kg}$ from $2.107 \mathrm{~kg}$

Here are the results of the subtractions:

(a) Subtracting ₹18.25 from ₹20.75 yields: **₹2.50**

(b) Subtracting $202.54 m$ from $250 m$ yields: **47.46 m**

(c) Subtracting ₹5.36 from ₹8.40 yields: **₹3.04**

(d) Subtracting $2.051 km$ from $5.206 km$ yields: **3.155 km**

(e) Subtracting $0.314 kg$ from $2.107 kg$ yields: **1.793 kg**

Find the value of : with steps

(a) $9.756-6.28$

(b) $21.05-15.27$

(c) $18.5-6.79$

(d) 11.6 - 9.847

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Raju bought a book for ₹ 35.65 . He gave ₹ 50 to the shopkeeper. How much money did he get back from the shopkeeper?

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Rani had ₹ 18.50 . She bought one ice-cream for ₹ 11.75 . How much money does she have now?

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Tina had $20 \mathrm{~m} 5 \mathrm{~cm}$ long cloth. She cuts $4 \mathrm{~m} 50 \mathrm{~cm}$ length of cloth from this for making a curtain. How much cloth is left with her?

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Namita travels $20 \mathrm{~km} 50$ m every day. Out of this she travels $10 \mathrm{~km} 200 \mathrm{~m}$ by bus and the rest by auto. How much distance does she travel by auto?

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Aakash bought vegetables weighing $10 \mathrm{~kg}$. Out of this, $3 \mathrm{~kg} 500 \mathrm{~g}$ is onions, $2 \mathrm{~kg} 75 \mathrm{~g}$ is tomatoes and the rest is potatoes. What is the weight of the potatoes?