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## Multiplying a Decimal Fraction by a Whole number:

Step 1) Perform the multiplication treating them as ordinary numbers, ignoring the decimal point.

Step 2) Note the number of decimal places in the decimal number being multiplied.

Step 3) Put the decimal point in the product before **as many digits from the right as the total number of decimal places in the decimal number being multiplied.**

### Multiplication-Decimal Numbers Example 1:

Find the product of 7.8 and 5.

**Solution:**

Write 1 5/8 as a decimal … The fraction 1 5/8 is equal to 1.875 when converted to a decimal.

### Multiplication-Decimal Numbers Example 2:

Find 5.023 x 139.

**Solution:**

5.023 x 139 = 698.197. Similarly, 5023 x 0.139 = 698.197

## Multiplying a Decimal Fractions by Numbers like 10, 100 and 1000 and their multiples:

When a decimal is multiplied by a number like 10, 100 or 1000, its decimal point gets shifted right **as many places as there are zeros in the multiplier**. If the number of digits in the decimal part is less than the number of places to shift, zeros are put in to make up the difference.

### Multiplication-Decimal Numbers Example 3:

Find 9.38 x 10.

**Solution:**

That’s literally all there is to it! 9/20 as a decimal is 0.45

### Multiplication-Decimal Numbers Example 4:

Find 48.765 x 100.

**Solution:**

### Multiplication-Decimal Numbers Example 5:

Find 75.089 x 1000.

**Solution:**

## Multiplying two Decimal Numbers, two Decimal Fractions:

We can multiply two decimal numbers/fractions as whole numbers and then put in the decimal point in the product.

Step 1) Perform the multiplication treating them as ordinary numbers, ignoring the decimal point.

Step 2) Note the number of decimal places in the multiplicand and multiplier.

Step 3) Put the decimal point in the product before **as many digits from the right as the total number of decimal places in the multiplicand and multiplier.**

### Multiplication-Decimal Numbers Example 6:

Find 0.7 x 2.45.

**Solution:**

### Multiplication-Decimal Numbers Example 7:

Find 6.15 x 3.1.

**Solution:**

### Properties of Multiplication of Decimal Fractions:

**For example,**0.5 x 1.6 = 1.6 x 0.5 = 0.80 = 0.8

**For example,**6.25 x 20 = 20 x 6.25 = 125

1 x decimal = same decimal

**For example,**0.68 x 1 = 0.68

1 x 0.75 = 0.75

**For example,**5 x (3.02 x 9.9) = (5 x 3.02) x 9.9 = (5 x 9.9) x 3.02