# Free Knowing Our Numbers Subjective Test 01 Practice Test - 6th grade

The height of a person is 1m 65cm. What is his height in millimeters? [1 MARK]

#### SOLUTION

Solution :
We know that,
1m = 1000 mm
1cm = 10 mm
65 cm = 65×10 = 650mm
The height of the person = 1000 + 650 = 1650mm

An uncle gave Rs.1001 to Rahul and Rs.1501 to Shweta. Who has more money and by how much? [2 MARKS]

#### SOLUTION

Solution :

Concept: 1 Mark
Solution: 1 Mark
Shweta has more money than Rahul. If we compare both the numbers, then
the number with the greater valued digit on the extreme left will be greater. 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, Rs.1501 is greater than Rs.1001. Now,1501-1001 = 500
Shweta has Rs 500 more than Rahul.

Shubhangi bought a beautiful lehenga, the price of which is equal to the greatest 5-digit number. What is the price of the lehenga? [2 MARKS]

#### SOLUTION

Solution :

Concept: 1 Mark
Solution: 1 Mark
If we want to find the greatest 5 digit number, we will use the greatest digit, which is 9, in each place value, of all the five digits.
Hence, the price of the lehenga is 99,999, which is the largest five digit number.

Shweta while giving an exam saw question no.XIV in her question paper. How can she find out what number is XIV? [3 MARKS]

#### SOLUTION

Solution :

Concept: 1 Mark
Application: 2 Marks

If a symbol of smaller value is written between the symbols of greater value, then its value is subtracted from the symbol of the greater value which is written immediately after the symbol of the smaller value. For example the value of XIV is 10 + (5 - 1) i.e. 14.

Aashu's elder sister asked him to make the smallest number using the digits of 8734. What is the number? Also, find the sum of these numbers. [3 MARKS]

#### SOLUTION

Solution :

Concept: 1 Mark
Application: 1 Mark
Solution: 1 Mark

The smallest number Aashu arrived at using 8734 is 3478.

He did so by following the below steps:

(a) The smallest digit is placed at one's place.

(b) The next greater digit is placed at ten's place.

(c) The next greater digit is placed at hundred's place and so on.

(d) The greatest digit is placed at the highest place of the number.

Sum  = 8734 + 3478 = 12221

The distance between Ranchi and Kolkata is 420 km. David took a flight from Bangalore to Ranchi via Kolkata. The distance between Banglore and Kolkata is 400 km. Find the total distance travelled by David in metres. [3 MARKS]

#### SOLUTION

Solution :

Concept: 1 Mark
Steps: 1 Mark

1km = 1000m
Distance between Ranchi and Kolkata = 420 km= 420 ×1000 = 420000m
Distance between Bangalore and Kolkata = 400 km = 400 ×1000 = 400000m
The total distance travelled by David = 400000 + 420000 = 820000m

Yuvraj was asked to estimate the sum of 4689 + 19316 and 108 + 2499. Explain with proper steps. [4 MARKS]

#### SOLUTION

Solution :

Concept: 1 Mark
Steps: 2 Marks

Given that
We have to estimate 4689 + 19316

Clearly, 19316 > 4689
we shall round off the numbers to the nearest thousands.
19316 is rounded off to 19000
4689 is rounded off to 5000

Estimated sum is:
19000 + 5000 = 24000
We also have to estimate:

108 + 24999
Now, 24999 > 108
We shall round off the number to nearest hundred.
108 can be rounded off to 100.
24999 can be rounded off to 25000.
The estimated sum of the numbers = 100 + 25000 = 25100.

Anshul bought 94 t-shirts each of ₹ 576, while Prakash bought 49 t-shirts for ₹ 499 each. What is the total estimated price Anshul and Prakash have to pay?  Also, find the exact amount to be paid by both of them. [4 MARKS]

#### SOLUTION

Solution :

Concept: 1 Mark
Steps: 2 Marks
Solution: 1 Mark

Anshul has to pay ₹ (94 × 576).

The first number, 94, can be rounded off to the nearest ten as 90.
The second number, 576, can be rounded off to the nearest hundred as 600.
Hence, the estimated price of the product = 90 × 600 = ₹ 54,000
The actual price=94×576 = (90+4)×(600-24) = (90×600-90×24 + 4×600-4×24) = (54000-2160+2400-96) =
54144

Prakash has to pay  (49×499).
The first number 49 can be rounded off to the nearest ten as 50.
The second number 499 can be rounded off to the nearest hundred as 500.
The estimated price of the product is 50×500 =  25000
The actual price= 49×499 = (50-1)×(500-1) = (50×500-50×1 -1×500+1×1) = (25000 - 50 - 500 + 1) = 24451

What happens
(i) if a symbol of smaller value is written to the right of a symbol of greater value?
(ii) if a symbol of smaller value is written to the left to the left of a symbol of greater value?
Explain with the help of examples. [4 MARKS]

#### SOLUTION

Solution :

Steps: 2 Marks
Example: 2 Marks

(i) 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.
For example, let us take VI. Here, the value of V in decimal value = 5
And the value of I in decimal value = 1
Now, 5 > 1, the left part is greater than the right part.
So we will add the value of the smaller value of the greater one.
The decimal value of VI = 5 + 1 = 6

(ii) If a symbol of smaller value is written to the left of a symbol of greater value, its value is subtracted from the value of the greater symbol.
For example, let us take IX.
Here, the decimal value X = 10
While the decimal value if I = 1
10>1, the value on the left is greater than the value on the right.
So the decimal value of IX = 10 - 1 = 9.

But we need to be a little careful while using this rule.
The symbols, V, L, and D are never written to the left of a symbol of greater value, i.e. V, L, and D are never subtracted.

Make the greatest and the smallest 5-digit numbers using different digits in which 5 appears at ten’s place. Also, find their sum. [4 MARKS]

Solution :

Concept: 1 Mark
Steps: 2 Marks