DECIMALS

When we have fractions in tenths, hundredths or thousandths, we can express them in decimal fractions. We can write 7/10 or seven-tenths in this form: 0.7.

Similarly, 7/100 = 0.07 and 7/1000 = 0.007.

Points to remember:

1. When the denominator of a fraction is 10, we have only one place of decimal, example 3/10 = 0.3.
2. When the denominator of a fraction is 100, we have two places of decimal, example 3/100 = 0.03.
3. When the denominator of a fraction is 1000, we have three places of decimal, example 3/1000 = 0.003, and so on.

Note: The zeros placed between the decimal point and the numbers are very important as they show the different values.

Value and Place Value

 Whole Numbers Decimals Thousands 2 Hundreds 3 Tens 4 Ones 5 · Tenths 6 Hundredths 7 Thousandths 8

A point called the decimal point separates the fractional parts i.e. tenths, hundredth, etc from the whole-number parts.

Value

1. The value of 6 in 2 345.678 is 6 tenths or 6/10.
2. The value of 7 in 2 345.678 is 7 hundredths or 7/100.
3. The value of 8 in 2 345.678 is 8 thousandths or 8/1000.

Place Value

In 2 345.678,
the digit 6 is in the tenths place,
the digit 7 is in the hundredths place, and
the digit 8 is in the thousandths place.

In the addition and subtraction of decimals, we must arrange the digits according to their values.

Examples:

1. What is the sum of 25.34, 20.3 and 5?
2.  25.34 2.30 + 5.00 32.64
3. What is the difference between 8.68 and 14?
 14.00 - 8.68 5.32

Note: The decimal points are arranged in a straight line to show the values of the digits.

In the multiplication of any two decimals, we multiply the numbers as though they are whole numbers. Then we insert the decimal point by counting the total number of decimal places in the two numbers.

Example: Find the product of 7.9 and 3.6

 7.9 (1 decimal place) x  3.6 (1 decimal place) 474 + 2370 28.44 (2 decimal places)

In the division of decimals, we follow the same process as we divide with whole numbers. Place the decimal point of the quotient above the decimal point of the dividend.

Example: Divide 60.48 by 9.

6.72 --> Quotient
Divisor --> 9 )  60.48 --> Dividend

When multiplying or dividing decimals by 10, 100 or 1 000, the numbers remain unchanged but the decimal point is moved.

Examples:

1. 12.345 x 10 (move the decimal point 1 place to the right)
= 123.45

2. 12.345 x 100 (move the decimal point 2 places to the right)
= 1 234.5

3. 12.345 x 1 000 (move the decimal point 3 places to the right)
= 12 345

4. 12.345 ÷ 10 (move the decimal point 1 place to the left)
= 1.234 5

5. 12.345 ÷ 100 (move the decimal point 2 places to the left)
= 0.123 45

6. 12.345 ÷ 1 000 (move the decimal point 3 places to the left)
= 0.012 345

Problems on Decimals

Examples:

1. Mr Wu had a plank 6.4 m long. He then cut 0.4 of it out. What was the length of  the plank left?

1 - 0.4 = 0.6
0.6 of the plank was left.

0.6 x 6.4 = 3.84
3.84 m of the plank was left.

2. Meili gets \$5.40 per week as pocket money. This is 60 cents more than Fatimah's weekly pocket money. Find the total pocket money the two girls get in 5 weeks.

\$5.40-\$0.60 = \$4.80 …………………………….. (a)

Fatimah gets \$4.80 every week.

\$5.40 + \$4.80 = \$10.20 ………………………… (b)

They both get \$10.20 in one week.

5 x \$10.20 = \$51

Their total pocket money in 5 weeks is \$51.