8
0
a
+ 3 2 3 6 0
(d) 2,568 x 30
(e) The standard for
+40 + 9
4 0 4 50
So, the multiplication using expanded form is correct
Exercise 4.1
struct the multiplication tables of the following numbers a
Multiplication tables of 12 and 15 using repeated additi
Multiplication tables of 14 and 17 using skip countinjg
Multiplication tables of 18 and 20 by adding 1 to 10
Answers
Hi , I didn't understand the question can you tell me again ?
Answer:
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Expanded form of Decimal Fractions
We will discuss here about the expanded form of decimal fractions.
In expanded form of decimal fractions we will learn how to read and write the decimal numbers.
Decimal numbers can be expressed in expanded form using the place-value chart. Let us consider the number 561.129. Let us expand each of the digits using the place-value chart.
Expanded form of Decimal
7Save
So, we can write 561.129 in the expanded form as follows.
561.129 = 500 + 60 + 1 + 0.1 + 0.02 + 0.009
= 5 hundreds + 6 tens + 1 ones + 1 tenths + 2 hundredths + 9 thousandths
= 500 + 60 + 1 + 1/10 + 2/100 + 9/1000
Again,
493.2 = 4 hundreds + 9 tens + 3 ones + 2 tenths
= 400 + 90 + 3 + 2/10
1436.74 = 1 thousands + 4 hundreds + 3 tens + 6 ones + 7 tenths + 4 hundredths
= 1000 + 400 + 30 + 6 + 7/10 + 4/100
Note: When a decimal is missing either in the integral part or decimal part, substitute with 0.
1. Write in expanded form:
(i) 3479.105
= 3 thousands + 4 hundreds + 7 tens + 9 ones + 1 tenths + 0 hundredths+ 5 thousandths
= 3000 + 400 + 70 + 9 + 1/10 + 0/100 + 5/1000
(ii) 7833.45
= 7 thousands + 8 hundreds + 3 tens + 3 ones + 4 tenths + 5 hundredths
= 7000 + 800 + 30 + 3 + 4/10 + 5/100
(iii) 21.1097
= 2 tens + 1 ones + 1 tenths + 0 hundredths + 9 thousandths + 7 ten thousandths
= 20 + 1 + 1/10 + 0/100 + 9/1000 + 7/10000
(iv) 524.1
= 5 hundreds + 2 tens + 4 ones + 1 tenths
= 500 + 20 + 4 + 1/10
(v) 143.011
= 1 hundreds + 4 tens + 3 ones + 0 tenths + 1 hundredths + 1 thousandths
= 100 + 40 + 3 + 0/10 + 1/100 + 1/1000
(vi) 840.006
= 8 hundreds + 4 tens + 0 ones + 0 tenths + 0 hundredths + 6 thousandths
= 800 + 40 + 0 + 0/10 + 0/100 + 6/1000
(vii) 64.21
= 6 tens + 4 ones + 2 tenths + 1 hundredths
= 60 + 4 + 2/10 + 1/100
(viii) 4334.334
= 4 thousands + 3 hundreds + 3 tens + 4 ones + 3 tenths + 3 hundredths + 4 thousandths
= 4000 + 300 + 30 + 4 + 3/10 + 3/100 + 4/1000
2. Write as decimal fractions:
(i) 8 thousands + 8 ones + 3 tenths + 9 hundredths
= 8008.39
(ii) 4000 + 7 + 5/10 + 6/100
= 4007.56
(iii) 6 hundreds + 9 tens + 8 tenths + 4 thousandths
= 690.804
(iv) 3 tens + 7 ones + 6 hundredths + 8 thousandths
= 37.068
(v) 400 + 50 + 1 + 9/100
= 451.09
(vi) 800 + 70 + 2 + 8/10 + 5/1000
= 872.805
(vii) 6 tens + 5 tenths + 8 hundredths
= 60.58
(viii) 9 hundreds + 4 tens + 3 tenths + 4 hundredths
= 940.34
3. Write the following in short form.
(i) 100 + 0.5 + 0.06 + 0.008 (ii) 80 + 1 + 0.02 + 0.005
Solution:
(i) 100 + 0.5 + 0.06 + 0.008
= 100.568
(ii) 80 + 1 + 0.02 + 0.005
= 81.025
4. Write the place-value of the underlined digits.
(i) 2.47 (ii) 11.003 (iii) 5.175
Solution:
(i) 2.47
Place-value of 7 in 2.47 is 7 hundredths or 0.07.
(ii) 11.003
Place-value of 3 in 11.003 is 3 thousandths or 0.003.
(iii) 5.175
Place-value of 1 in 5.175 is 1 tenths or 0.1.
Practice Problems on Expanded Form of Decimal Fractions:
I. Write the given decimals in expanded form by fractional expansion.
One example has been done for you to get the idea how to do decimals in expanded form by fractional expansion.
1.73 = 1 + 710 + 3100
(i) 23.8
(ii) 60.27
(iii) 119.05
(iv) 276.207
Answers:
(i) 20 + 3 + 810
(ii) 60 + 0 + 210 + 7100
(iii) 100 + 10 + 9 + 0 + 5100
(iv) 200 + 70 + 6 + 210 + 0 + 7100
II. Write the given decimals in expanded form by decimal expansion.
One example has been done for you to get the idea how to do decimals in expanded form by decimal expansion.
8.461 = 8 + 0.4 + 0.06 + 0.001
(i) 6.08
(ii) 36.505
(iii) 402.613
(iv) 700.037
Answers:
(i) 6 + 0.0 + 0.08
(ii) 30 + 6 + 0.5 + 0.00 + 0.005
(iii) 400 + 0 + 2 + 0.6 + 0.01 + 0.003
(iv) 700 + 0 + 0 + 0.0 + 0.03 + 0.007
III. Write the decimal number for the expansions given below.
(i) 10 + 6 + 310 + 91000
(ii) 600 + 20 + 7 + 110 + 3100 + 71000
(iii) 2000 + 8 + 310 + 9100
(iv) 400 + 70 + 1 + 0.5 + 0.07 + 0.002
(v) 5000 + 80 + 0 + 0.2 + 0.002
Answers:
(i) 16.309
(ii) 627.137
(iii) 2008.39
(iv) 471.572
(v) 5000 + 80 + 0 + 0.2 + 0.002 5080.202