Expanded form of Decimal Fractions

This topic will deal with expanded form of decimal numbers. We know that decimal numbers are numbers having a whole number part and a fractional part. The whole number part is separated from the fractional part by giving a dot (which is the decimal point). Now here in this section we will learn expanding of decimal number.

For example:

458.52

= 4 hundreds + 5 tens + 8 ones + 5tenths + 2 hundredths

After the decimal point each number is divided by 10, 100, 1000 and so on and so forth. That is why we write tenths, hundredths, thousandths…etc.

The whole number part is expanded in the same way as we expand whole numbers. 

Here are few more examples:

Expand the following decimal numbers:

(i) 471.235

4 hundreds + 7 thousands + 1 ones + 2 tenths + 3 hundredths + 5 thousandths

(ii) 9542.023

9 thousands + 5 hundreds + 4 tens + 2 ones + 0 tenths + 2 hundredths + 3 thousandths

(iii) 520.326

5 hundreds + 2 tens + 0 ones + 3 tenths + 2 hundredths + 6 ones

(iv) 1120.70

1 thousands + 1 hundreds + 2 tens + 0 ones + 7 tenths + 0 hundredths

(v) 123.520

1 hundreds + 2 tens + 3 ones + 5 tenths + 2 hundredths + 0 thousandths

(vi) 4140.237

4 thousands + 1 hundreds + 4 tens + 0 ones + 2 tenths + 3 hundredths + 7 thousandths

(vii) 94.007

9 tens + 4 ones + 0 tenths + 0 tenths + 0 hundredths + 7 thousandths

(viii) 7452.21

7 thousands + 4 hundreds + 5 tens + 2 ones + 2 tenths + 1 hundredths

(ix) 1754.009

1 thousands + 7 hundreds + 5 tens + 4 ones + 0 tenths + 0 hundredths + 9 thousandths

(x) 7.0056

7 ones + 0 tenths + 0 hundredths + 5 thousandths + 6 ten thousandths

Write the following expanded notation in decimal form:

(i) 4 hundreds + 6 tens + 2 ones + 9 hundredths + 2 thousandths

462.092

Here the tenths number is missing and hence it should be replaced with 0. It is actually 0 tenths.

(ii) 5 thousands + 6 hundreds + 8 tens + 7 ones + 2 thousandths

5687.002

Here again the tenths and hundredths number is missing that should be replaced with 0. It is actually 0 tenths and 0 hundredths.

(iii) 6 ten thousands + 8 thousands + 7 hundreds + 3 ones + 2 tenths + 3 hundredths + 5 thousandths

6873.235

(iv) 2 hundreds + 1 tens + 0 ones + 7 tenths + 2 hundredths + 8 thousandths

210.728

(v) 6 thousands + 2 hundreds + 2 tens + 0 ones + 5 tenths + 4 hundredths + 0 thousandths

6220.54

(vi) 1 hundreds + 6 tens + 0 ones + 5 hundredths + 2 thousandths

160.052

Here the tenths number is missing and hence it should be replaced with 0. It is actually 0 tenths.

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