Download Class 5 Decimal Numbers

ID : in-5-Decimal-Numbers [1]
Class 5
Decimal Numbers
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Answer t he quest ions
(1)
What do you get when you subtract the sum of 661.15 and 26.32 f rom 736.81?
(2)
Which number is 71.16 larger than the largest 4-digit number?
(3)
What do you get when you multiply 6.5 and 9.42?
(4) Fill in the blank with < , > , or = sign:
0.000606 ____ 0.0616
(5)
What do you get when you add the f ollowing decimals: 325.33 and 5.89?
Choose correct answer(s) f rom given choice
(6) T he place value of 7 in 1860.7425 is
a. 7 T enths
b. T housandths
c. 7 Hundreds
d. 7 T en thousandths
(7) What number do you get by adding 2 T housandths and 95 T en thousandths together to 21 T en
T housands?
(8)
a. 210003.8115
b. 210000.0115
c. 21000001.15
d. 2100.000115
T ake away One T enths seven times f rom 1 and you are lef t with
a. 0.1
b. 0.3
c. 0.7
d. none of these
(9) At a construction site, there are 13.5 loads of bricks, and the total weight of all the loads
together is 311.445 kgs. What is the weight of one load?
a. 22.89 kg
b. 23.14 kg
c. 23.07 kg
d. 23.18 kg
(10) Which of the f ollowing represents the number two Hundredths in decimal f orm
a. 0.02000
b. 0.000200
c. 0.20000
d. 2.00000
(11) Shilpa drove 44.802 kms to visit her grandmother. When she reached her grandmother's house
she noticed the car had used up 3.93 litres of petrol. How many kilometers did she travel per litre
of petrol?
a. 11.38 km
b. 11.4 km
c. 11.56 km
d. 11.26 km
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ID : in-5-Decimal-Numbers [2]
Fill in t he blanks
(12) A snail crawls 23 cm in 15 minutes. It crawls another 57 cm in 38 minutes. T he total distance it
crawls is
(13)
metres.
127.88 + 40.79 + 0.2 =
(14) How is the number thirty-one and sixteen T en thousandths written in decimal f orm as
(15) Meenakshi bought the f ollowing things when she got her f irst salary of Rs.60000
A gaming system f or Rs.2276.95
A microwave f or Rs.6167.05
A computer f or Rs.21970.50.
Now Rs.
is lef t with her.
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ID : in-5-Decimal-Numbers [3]
Answers
(1)
49.34
Step 1
Let us f irst f ind the sum of the Like Decimal numbers 661.15 and 26.32. Decimals with the
same number of decimal places are called Like Decimals.
Step 2
Let us add starting f rom the hundredths and carry over if needed. T he decimal point in the
answer will be placed as being placed in the addends:
T en T housands T housands Hundreds T ens Ones . T enth Hundredth
6
+
6
6
1
.
1
5
2
6
.
3
2
8
7
.
4
7
Step 3
Let us now subtract the sum 687.47 f rom 736.81 by placing the digits of these two Like
Fractions according to their place values
T en T housands T housands Hundreds T ens Ones . T enth Hundredth
-
7
3
6
.
8
1
6
8
7
.
4
7
0
4
9
.
3
4
Step 4
Hence, when we subtract the sum of 661.15 and 26.32 f rom 736.81, we get 49.34.
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ID : in-5-Decimal-Numbers [4]
(2)
10070.16
Step 1
T he largest 4-digit number is 9999 (a whole number).
Step 2
T he number 71.16 larger than 9999 can be f ound by adding the numbers 71.16 and 9999.
Step 3
Let us f irst convert the whole number 9999 into decimal f orm. In decimal f orm, 9999 can be
written as 9999.00. Decimals with the same number of decimal places are called like
decimals.
Step 4
Now, our task is to add the Like Decimals 71.16 and 9999.00. Let us add them starting f rom
the hundredths and carry over if needed. T he decimal point in the answer will be placed as
being placed in the addends:
Hundred
T housands
T en
T housands
T housands Hundreds T ens Ones . T enth Hundredth
9
9
+
1
0
0
9
9
.
0
0
7
1
.
1
6
7
0
.
1
6
Step 5
Hence, the number 71.16 larger than the largest 4-digit number is 10070.16.
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ID : in-5-Decimal-Numbers [5]
(3)
61.230
Step 1
In order to multiply the two decimal numbers, let us f irst f ind out the position of the decimal
point in the f inal product.
Step 2
Let us f irst count the number of decimal places in both the multiplicands. T he total number
of decimal places in the product will be the sum of the number of decimal places in both the
multiplicands.
Step 3
In the number 6.5, there is 1 decimal place and in 9.42 there are 2 decimal places.
Hence, there will be a total of 3 decimal places in the f inal product.
Step 4
Now, let us multiply the two numbers just like whole numbers, and in the f inal product place
the decimal point such that there are 3 decimal places (i.e. af ter 3 places f rom the right):
9 4 2
x 6 5
4 7 1 0
5 6 5 2 0
6 1 2 3 0
Step 5
Now put the decimal point af ter three places f rom right. T heref ore,
9.42 × 6.5 = 61.230
(4) <
Step 1
In the given problem we must f irst compare the whole numbers. Here, we see that the whole
part f or both the numbers is ‘0’ and hence is equal.
Step 2
However, we know that the given two numbers are not equal. So, let us compare the
f ractional part.
Step 3
Comparing the f ractional part of the two numbers, we f ind that .000606 < .0616.
Step 4
Hence, 0.000606 < 0.0616.
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ID : in-5-Decimal-Numbers [6]
(5)
331.22
Step 1
Decimals with the same number of decimal places are called Like Decimals. T he numbers
given here are theref ore Like Decimals.
Step 2
In order to add the given Like Decimals, let us arrange the digits according to their place
value, that is one below the other to make sure that the decimals are also placed exactly
one below the other. T his way, we will place the ones below the ones, the tenths below the
tenths and so on.
Step 3
T he decimal point in the answer will be placed as being placed in the addends.
Step 4
Let us add the numbers digit by digit starting f rom the hundredths and carry over if needed:
T housands Hundreds T ens Ones . T enth Hundredth
3
2
+
3
3
5
.
3
3
5
.
8
9
1
.
2
2
Step 5
Hence, when we add the decimals 325.33 and 5.89, we get 331.22.
(6) a. 7 T enths
Step 1
Let’s use the place value chart and f ind where 7 is placed: 18607425
| Lakhs| T housands|
| T L| L|
Ones| T enths| Hundredths| T housandths| T en thousandths|
T T H| T H| H| T | O| . (1/10)|
1
8 6 0 .
7
(1/100)|
4
(1/1000)|
2
(1/10000)|
5
Legend:
T L - T en Lakhs, L - Lakhs, T T H - T en T housands, T H - T housands, H - Hundreds, T T ens, O - Ones.
Step 2
From the above table, we observe that 7 is placed under the T enths place.
Step 3
Hence, the place value of 7 in 1860.7425 is 7 T enths.
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ID : in-5-Decimal-Numbers [7]
(7) b. 210000.0115
Step 1
Let us f irst convert the number names into numerals:
2 T housandths = 2 ÷ 1000 = 0.002
95 T en thousandths = 95 ÷ 10000 = 0.0095
21 T en T housands = 21 × 10000 = 210000
Step 2
Let’s f irst add the decimal numbers as below:
| T housands|
Lakhs|
| T L| L|
Ones| T enths| Hundredths| T housandths| T en thousandths|
T T H| T H| H| T | O| . (1/10)|
T otal
(1/100)|
(1/1000)|
(1/10000)|
0 .
0
0
2
0
0 .
0
0
9
5
0 .
0
1
1
5
Legend:
T L - T en Lakhs, L - Lakhs, T T H - T en T housands, T H - T housands, H - Hundreds, T T ens, O - Ones.
Step 3
Let us now add the decimal numbers with the whole number:
| T housands|
Ones| T enths| Hundredths| T housandths| T en thousandths|
Lakhs|
| T L| L|
T otal
T T H| T H| H| T | O| . (1/10)|
(1/100)|
(1/1000)|
(1/10000)|
0 .
0
1
1
5
2
1
0
0 0 0 .
0
0
0
0
2
1
0
0 0 0 .
0
1
1
5
Step 4
T heref ore, by adding 2 T housandths and 95 T en thousandths together to 21 T en
T housands, we get 210000.0115.
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ID : in-5-Decimal-Numbers [8]
(8)
b. 0.3
Step 1
Look at the question caref ully and notice that One T enths of 1 =
1
,
10
and seven times of
1
10
=
7
10
= 0.7
Step 2
Now take One T enths seven times f rom 1 or subtracting 0.7 f rom 1 = 1 - 0.7
= 0.3
Step 3
T heref ore the lef t value with you, when you take away One T enths seven times f rom 1 is
0.3.
(9) c. 23.07 kg
Step 1
T he number of loads of bricks = 13.5
Step 2
T otal weight of all the loads together = 311.445 kgs
Step 3
In order to f ind the weight of one load, we need to divide the total weight by the number of
loads.
Step 4
T heref ore, the weight of one load is 311.445 ÷ 13.5 = 23.07 kg.
(10) a. 0.02000
Step 1
Let’s f irst convert the number name into number/f raction. So, two Hundredths can be
written as:
2
100
Step 2
By converting the f raction into decimals, we get:
2
= 0.02
100
Step 3
T heref ore, the number two Hundredths in decimal f orm is 0.02.
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ID : in-5-Decimal-Numbers [9]
(11) b. 11.4 km
Step 1
Distance that Shilpa drove to reach her grandmother's house = 44.802 kms
Step 2
Number of litres used while driving = 3.93 litres
Step 3
In order to know the number of kilometres per litre of petrol, we will need to divide the
number of kilometers traveled Shilpa by the number of litres of petrol used.
Step 4
T hus, the number of kilometers Shilpa travelled per litre of petrol = 44.802 ÷ 3.93 = 11.4
km/litre
Step 5
T heref ore, the kilometres per litre of petrol (mileage of the car) is 11.4 km/liter.
(12)
0.8
Step 1
T he total distance (in cm) the snail crawls: 23 cm + 57 cm = 80 cm
Step 2
Let us now convert the distance 80 cm (centimetres) into distance in meters as below. We
know that:
100 cm = 1 m
T heref ore, 80 cm =
80
m = 0.8 m
100
Step 3
Hence, the snail crawls 0.8 m in the total time.
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ID : in-5-Decimal-Numbers [10]
(13)
168.87
Step 1
Decimals with the same number of decimal places are called Like Decimals. T he numbers
given here are theref ore Like Decimals.
Step 2
In order to add the given Like Decimals, let us arrange the digits according to their place
value, that is one below the other to make sure that the decimals are also placed exactly
one below the other. T his way, we will place the ones below the ones, the tenths below the
tenths and so on.
Step 3
T he decimal point in the answer will be placed as being placed in the addends.
Step 4
Let us add the numbers digit by digit starting f rom the hundredths and carry over if needed:
T housands Hundreds T ens Ones . T enth Hundredth
1
2
7
.
8
8
4
0
.
7
9
0
.
2
0
8
.
8
7
+
1
6
Step 5
Hence, when we add the decimals 127.88, 40.79, and 0.2 we get 168.87
(14)
31.0016
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ID : in-5-Decimal-Numbers [11]
(15)
29585.50
Step 1
Amount received by Meenakshi as salary = Rs.60000
Step 2
Let us add the amounts spent by Meenakshi f or purchasing various things:
T en
T housands Hundreds T ens Ones . T enth Hundredth
T housands
A gaming
2
2
7
6
.
9
5
6
1
6
7
.
0
5
system
A microwave
A computer
2
1
9
7
0
.
5
0
T otal
3
0
4
1
4
.
5
0
Expense
Hence, Meenakshi's total expense is Rs.30414.50.
Step 3
In order to f ind the amount lef t with Meenakshi, let us subtract her f irst salary with her total
expense:
Amount lef t with Meenakshi = Meenakshi's salary - Meenakshi's total expense
= 60000 - 30414.50
= 60000.00 - 30414.50 ...(Writing 60000 in decimal f orm 60000.00 so that the two numbers
are Like Decimals)
Step 4
Now, let us subtract 30414.50 f rom 60000.00 by placing the digits of two decimal numbers
according to their place values:
T en T housands T housands Hundreds T ens Ones . T enth Hundredth
-
6
0
0
0
0
.
0
0
3
0
4
1
4
.
5
0
2
9
5
8
5
.
5
0
Step 5
Hence, af ter shopping Meenakshi is lef t with Rs.29585.50.
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