HOW TO WRITE DECIMALS IN EXPANDED FORM

Expanded form :

Expanded form is the sum of each digit multiplied by its matching place value, whereas in expanded form, addition is only used between place value numbers.

To write a Decimal in expanded form, there are two methods.

Method 1 :

52.504

Step 1 :

Write the digits in the place values table.

Step 2 :

Write down the sum of each digit multiplied by its place value.

= (5 × 10) + (2 × 1) + (5 × 1/10) + (0 × 1/100) + (4 × 1/100)

= 50 + 2 + 5/10 + 4/100

Method 2 :

53.707

The decimal 53.707 can be expanded as,

= 50 + 3 + 0.7 + 0.007

= 50 + 3 + 7/10 + 7/1000

Express the following in Expanded Form :

Problem 1 :

3.6

Solution :

= 3.6

The decimal 3.6 can be expanded as,

= 3 + 0.6

= 3 + 6/10

Problem 2 :

8.07

Solution :

= 8.07

The decimal 8.07 can be expanded as,

= 8 + 0.07

= 8 + 7/100

Problem 3 :

0.123

Solution :

= 0.123

The decimal 0.123 can be expanded as,

= 0.1 + 0.02 + 0.003

= 1/10+ 2/100 + 3/1000

Problem 4 :

2.061

Solution :

= 2.061

The decimal 2.061 can be expanded as,

= 2 + 0.06 + 0.001 

= 2 + 6/100 + 1/1000

Problem 5 :

3.0071

Solution :

= 3.0071

The decimal 3.0071 can be expanded as,

= 3 + 0.007 + 0.0001 

= 3 + 7/1000 + 1/10000

Problem 6 :

0.00054

Solution :

= 0.00054

The decimal 0.00054 can be expanded as,

= 0.0005 + 0.00004 

= 5/10000 +4/100000

Problem 7 :

3.058

Solution :

= 3.058

The decimal 3.058 can be expanded as,

= 3 + 0.05 + 0.008 

= 3 + 5/100 + 8/1000

Problem 8 :

0.0632

Solution :

= 0.0632

The decimal 0.0632 can be expanded as,

= 0.06 + 0.003 + 0.0002

= 6/100 + 3/1000 + 2/10000

Problem 9 :

0.00607

Solution :

= 0.00607

The decimal 0.00607 can be expanded as,

= 0.006 + 0.00007

= 6/1000 + 7/100000 

Problem 10 :

Write each decimal as a fraction, and write the name of the decimal in word form. The first one is done for you.

Solution :

a)  0.244

Converting into fraction :

Since we have three digits after the decimal, we should multiply and divide by 1000.

= 0.244 x (1000/1000)

= 244/1000

Converting into word form :

Two fourty four thounsandths.

b) 0.65

Converting into fraction :

Since we have three digits after the decimal, we should multiply and divide by 100.

= 0.65 x (100/100)

= 65/100

Converting into word form :

Sixty five hundredth

c) 0.003

Converting into fraction :

Since we have three digits after the decimal, we should multiply and divide by 1000.

= 0.003 x (1000/1000)

= 3/1000

Converting into word form :

Three thounsandths.

d) 0.8

Converting into fraction :

Since we have three digits after the decimal, we should multiply and divide by 10.

= 0.8 x (10/10)

= 8/10

Converting into word form :

Eight tenth

f) 0.045

Converting into fraction :

Since we have three digits after the decimal, we should multiply and divide by 1000.

= 0.045 x (1000/1000)

= 45/1000

Converting into word form :

Forty five thousandths.

g) 0.781

Converting into fraction :

Since we have three digits after the decimal, we should multiply and divide by 1000.

= 0.781 x (1000/1000)

= 781/1000

Converting into word form :

Seven hundred and eighty one thousandths.

Problem 11 :

Write each decimal as a fraction.

a) 0.42

b) 0.079

c) 0.396

d) 0.403

Solution :

a) 0.42

The numerals at

• tenth place = 4, then 4/10
• hundredth place = 2, then 2/100

Expanded form :

4/10 + 2/100

b) 0.079

The numerals at

• tenth place = 0
• hundredth place = 7, then 7/100
• thousandth place = 9, then 9/100

Expanded form :

7/100 + 9/1000 

c) 0.396

The numerals at

• tenth place = 3, then 3/10
• hundredth place = 9, then 9/100
• thousandths place = 6, then 6/1000

Expanded form :

3/10 + 9/100 + 6/1000

d) 0.403

The numerals at

• tenth place = 4, then 4/10
• hundredth place = 0, then 0/100
• thousandth place = 3, then 3/1000

Expanded form :

4/10 + 0 + 3/1000

Problem 12 :

Yolanda wrote a number.

• The digit in the millions place is an 8.
• The digit in the thousands place is a 6.
• The digit in the hundredths place is a 2.

Which number could be the number Yolanda wrote?

a) 85,346,000.12      b) 38,056,000.21      c)  58,346,000.12    d)  98,674,200.21

Solution :

Option a :

85,346,000.12

Here,

• The digit in the millions place is 3

So, option a is incorrect.

Option b :

38,056,000.21 

Here,

• The digit in the millions place is an 0

So, option b is incorrect.

Option c :

58,346,000.12

Here,

• The digit in the millions place is 8 (58,346,000.12)
• The digit in the thousands place is a 6. (58,346,000.12)
• The digit in the hundredths place is a 2.(58,346,000.12)

So, option c is correct.

Problem 13 :

Write as decimal :

a)  400 + 60 + 5 + 0.2 + 0.09

b)  30 + 2 + 0.7 + 0.03

c)  50 + 4 + 2/10 + 8/100

d)  200 + 10 + 5 + 1/10 + 4/1000

Solution :

a)  400 + 60 + 5 + 0.2 + 0.09

= 465.29

b)  30 + 2 + 0.7 + 0.03

= 32.73

c)  50 + 4 + 2/10 + 8/100

= 54.28

d)  200 + 10 + 5 + 1/10 + 4/1000

= 215.14