# Free Knowing Our Numbers Subjective Test 02 Practice Test - 6th grade

Srishti found Rs.2000 fallen on the road. Megha found Rs.3000 next day at the same place. Who is richer? [1 MARK]

#### SOLUTION

Solution :

When we are comparing two numbers, either of the two things can happen.
i. One of the numbers has a greater number of digits. or
ii. Both the numbers have the equal number of digits.
When one of the numbers has a greater number of digits, then the one which has a greater number of digits is greater.

If the number of digits is equal, then the following steps are followed:
i. The number with the greater valued digit on the extreme left is greater.
ii. If the digits on the extreme left of the numbers are equal, then the digits to the right of the extreme left digits are compared and so on.
Therefore, Megha is rich right now.

Among all the natural numbers, which is the smallest and the largest natural number? [2 MARKS]

#### SOLUTION

Solution :

Natural Numbers: 1 Mark each

The smallest natural number is 1 and there is no largest natural number as we have infinite natural numbers.

Convert the following weights into grams.
a. 40 kg
b. 120 kg
[2 MARKS]

#### SOLUTION

Solution :

Each option: 1 Mark

1 Kilogram = 1,000 grams.

a. 40 Kilograms = 40 × 1000 = 40,000 grams.
b. 120 kilograms = 120 × 1000 = 1,20,000 grams.

Shalini has 1.5L of soda in a bottle. How many glasses can be filled, each of which has a capacity of 50 ml? How many glasses of capacity 60ml each be filled? [3 MARKS]

#### SOLUTION

Solution :

Concept: 1 Mark
Steps: 1 Mark

1L=1000ml
Capacity of bottle = 1.5 ×1000 = 1500ml

Capacity of glass = 50ml

Number of glasses that can be filled = 1500 ÷ 50 = 30 glasses
Now if the capacity of glasses = 60ml.
Then, the number of glasses that can be filled = 1500 ÷ 60= 25 glasses

Write in an expanded form? Place commas correctly for each of the numbers.

(a) 74836
(b) 574021
(c) 8907010
(d) 99999999
(e) 100001
(f) 545

[3 MARKS]

#### SOLUTION

Solution :
(a) 74,836 = 7 × 10000 + 4 × 1000 + 8 × 100 + 3 ×10 + 6 × 1

(b) 5,74,021 = 5 × 100000 + 7 × 10000 + 4 × 1000 + 2× 10 + 1×1

(c) 89,07,010 = 8 × 1000000 + 9 × 100000 + 7 × 1000 + 10 × 1

(d) 9,99,99,999 = 9×10000000 + 9×1000000 + 9×100000 + 9×10000 + 9×1000 + 9×100 + 9×10 + 9× 1

(e) 1,00,001 = 1×100000 + 0×10000 + 0×1000 + 0×100 + 0×10+1× 1

(f) 545 = 5×100 + 4×10 + 5 × 1

The population of a town was 78787 in the year 1991 and 95833 in the year 2001. Estimate the increase in population by rounding off each population to nearest hundreds. [3 MARKS]

#### SOLUTION

Solution :

Steps: 2 Marks

The population of a town in 1991 = 78787

and the population of that town in 2001 = 95833

78787 is rounded off the nearest hundreds

= 78800

95833 is rounded off to nearest hundreds

= 95800

Estimated increase in population

= 95800 – 78800 = 17000

Raj had Rs.1398 in his wallet. He left Rs.526 outside the movie counter. Estimate how much money is left with him.  Also, find the actual amount left with him, and the difference between the estimated and actual amount.[4 MARKS]

#### SOLUTION

Solution :

Steps: 2 Marks
Actual Amount: 1 Mark
Estimated Amount: 1 Mark

We need to estimate 1398 - 526.
1398 > 526.

we will round off these numbers to the nearest hundreds.
1398 can be rounded off to 1400.
526 can be rounded off to 500.

Estimated difference:
1400 - 500 = 900
The actual amount left with him= 1398 - 526 = 872
The difference between the estimated amount left to him, and the actual amount left with him=900 - 872 = 28.

What is the difference between the greatest and the least 5 digit number that can be written from 1, 3, 5, 7, 6? Also, find the difference between the greatest and the least 4 digit number that can be formed from them. [4 MARKS]

#### SOLUTION

Solution :

Concept: 1 Mark
Steps: 2 Marks

The given digits are 1,3,5,7,6.
Now to find the greatest number, we will arrange the given digits in descending order, i.e. the greatest number to the extreme left, then the next one and so on.
To find the smallest number, we will arrange the digits in an ascending order, i.e. the smallest number to the extreme left and so on.

Greatest number = 76531

Smallest number = 13567

Difference = 76531 - 13567 = 62964

Similarly,
The greatest 4 digit number that can be formed using the given digits = 7653
The least 4 digit number that can be used using the given digits = 1356
The difference between the greatest and the least=7653 - 1356 = 6297

The distance between Anshul's office and his house is 5.5 km. One day he went walking to office. While coming back, he walked for 2km and then took a cab. Find the total distance walked by Anshul in meters. [4 MARKS]

#### SOLUTION

Solution :

Concept: 1 Mark
Steps: 2 Marks

We know that ,1 km = 1000 m
Now total distance walked by Anshul = 5.5 (house to office) +2 km (way back from office)
Now 1 km = 1000m
5.5 km = 5.5 × 1000 = 5500 m
2 km = 2×1000 = 2000 m
Now total distance walked by Anshul = 5.5 + 2 km = 5500 + 2000 = 7500 m

Find the value of the following Roman numerals in decimal. Also, give a proper explanation for each step.
a) XXX
b) IX
c) VII
d) XII
[4 MARKS]

#### SOLUTION

Solution :

Each part: 1 Mark

a) XXX.
Now, we now that if a symbol is repeated, its value is added as many times as it occurs.
XXX = 10 + 10 + 10 = 30.

b) IX
I=1
X=10
1<10
If a smaller value is written to the left of a symbol of greater value, its value is subtracted from the value of the greater symbol.
The value IX = 10 - 1 = 9.

c) VII
If a symbol of smaller value is written to the right of a symbol of greater value, its value gets added to the value of the greater symbol.
V=5
I=1
The value of VII = 5 + 1 + 1 = 7.

d) XII
In this case, also, the smaller value is written to the right of the greater number. So its value is added to the value of the greater symbol.
XII= 10 + 1 + 1 = 12.